id	sid	tid	token	lemma	pos
ejpam-5300	1	1	european	european	PROPN
ejpam-5300	1	2	journal	journal	PROPN
ejpam-5300	1	3	of	of	ADP
ejpam-5300	1	4	pure	pure	ADJ
ejpam-5300	1	5	and	and	CCONJ
ejpam-5300	1	6	applied	apply	VERB
ejpam-5300	1	7	mathematics	mathematic	NOUN
ejpam-5300	1	8	vol	vol	NOUN
ejpam-5300	1	9	.	.	PROPN
ejpam-5300	2	1	17	17	NUM
ejpam-5300	2	2	,	,	PUNCT
ejpam-5300	2	3	no	no	INTJ
ejpam-5300	2	4	.	.	NOUN
ejpam-5300	2	5	4	4	NUM
ejpam-5300	2	6	,	,	PUNCT
ejpam-5300	2	7	2024	2024	NUM
ejpam-5300	2	8	,	,	PUNCT
ejpam-5300	2	9	4135	4135	NUM
ejpam-5300	2	10	-	-	SYM
ejpam-5300	2	11	4146	4146	NUM
ejpam-5300	2	12	issn	issn	PROPN
ejpam-5300	2	13	1307	1307	NUM
ejpam-5300	2	14	-	-	SYM
ejpam-5300	2	15	5543	5543	NUM
ejpam-5300	2	16	–	–	PUNCT
ejpam-5300	2	17	ejpam.com	ejpam.com	X
ejpam-5300	2	18	published	publish	VERB
ejpam-5300	2	19	by	by	ADP
ejpam-5300	2	20	new	new	PROPN
ejpam-5300	2	21	york	york	PROPN
ejpam-5300	2	22	business	business	PROPN
ejpam-5300	2	23	global	global	ADJ
ejpam-5300	2	24	generalizing	generalize	VERB
ejpam-5300	2	25	the	the	DET
ejpam-5300	2	26	equal	equal	ADJ
ejpam-5300	2	27	incircles	incircle	NOUN
ejpam-5300	2	28	theorem	theorem	VERB
ejpam-5300	2	29	:	:	PUNCT
ejpam-5300	2	30	insights	insight	NOUN
ejpam-5300	2	31	from	from	ADP
ejpam-5300	2	32	sangaku	sangaku	NOUN
ejpam-5300	2	33	problems	problem	NOUN
ejpam-5300	2	34	perawit	perawit	PROPN
ejpam-5300	2	35	boonsomchua	boonsomchua	PROPN
ejpam-5300	2	36	1engineer	1engineer	PROPN
ejpam-5300	2	37	science	science	NOUN
ejpam-5300	2	38	classroom	classroom	NOUN
ejpam-5300	2	39	(	(	PUNCT
ejpam-5300	2	40	esc	esc	NOUN
ejpam-5300	2	41	)	)	PUNCT
ejpam-5300	2	42	,	,	PUNCT
ejpam-5300	2	43	learning	learn	VERB
ejpam-5300	2	44	institute	institute	PROPN
ejpam-5300	2	45	,	,	PUNCT
ejpam-5300	2	46	king	king	PROPN
ejpam-5300	2	47	mongkut	mongkut	PROPN
ejpam-5300	2	48	’s	’s	PROPN
ejpam-5300	2	49	university	university	PROPN
ejpam-5300	2	50	of	of	ADP
ejpam-5300	2	51	technology	technology	PROPN
ejpam-5300	2	52	thonburi	thonburi	PROPN
ejpam-5300	2	53	,	,	PUNCT
ejpam-5300	2	54	bangkok	bangkok	PROPN
ejpam-5300	2	55	,	,	PUNCT
ejpam-5300	2	56	thailand	thailand	PROPN
ejpam-5300	2	57	abstract	abstract	PROPN
ejpam-5300	2	58	.	.	PUNCT
ejpam-5300	3	1	sangaku	sangaku	NOUN
ejpam-5300	3	2	problems	problem	NOUN
ejpam-5300	3	3	are	be	AUX
ejpam-5300	3	4	traditional	traditional	ADJ
ejpam-5300	3	5	japanese	japanese	ADJ
ejpam-5300	3	6	geometrical	geometrical	ADJ
ejpam-5300	3	7	puzzles	puzzle	NOUN
ejpam-5300	3	8	,	,	PUNCT
ejpam-5300	3	9	often	often	ADV
ejpam-5300	3	10	displayed	display	VERB
ejpam-5300	3	11	in	in	ADP
ejpam-5300	3	12	religious	religious	ADJ
ejpam-5300	3	13	temples	temple	NOUN
ejpam-5300	3	14	,	,	PUNCT
ejpam-5300	3	15	that	that	PRON
ejpam-5300	3	16	have	have	AUX
ejpam-5300	3	17	intrigued	intrigue	VERB
ejpam-5300	3	18	mathematicians	mathematician	NOUN
ejpam-5300	3	19	for	for	ADP
ejpam-5300	3	20	centuries	century	NOUN
ejpam-5300	3	21	.	.	PUNCT
ejpam-5300	4	1	this	this	DET
ejpam-5300	4	2	study	study	NOUN
ejpam-5300	4	3	aims	aim	VERB
ejpam-5300	4	4	to	to	PART
ejpam-5300	4	5	generalize	generalize	VERB
ejpam-5300	4	6	the	the	DET
ejpam-5300	4	7	equal	equal	ADJ
ejpam-5300	4	8	incircles	incircle	NOUN
ejpam-5300	4	9	theorem	theorem	VERB
ejpam-5300	4	10	,	,	PUNCT
ejpam-5300	4	11	extending	extend	VERB
ejpam-5300	4	12	angela	angela	PROPN
ejpam-5300	4	13	drei	drei	PROPN
ejpam-5300	4	14	’s	’s	PART
ejpam-5300	4	15	proof	proof	NOUN
ejpam-5300	4	16	to	to	ADP
ejpam-5300	4	17	n	n	DET
ejpam-5300	4	18	-circles	-circle	NOUN
ejpam-5300	4	19	,	,	PUNCT
ejpam-5300	4	20	by	by	ADP
ejpam-5300	4	21	applying	apply	VERB
ejpam-5300	4	22	the	the	DET
ejpam-5300	4	23	trigonometric	trigonometric	ADJ
ejpam-5300	4	24	method	method	NOUN
ejpam-5300	4	25	alongside	alongside	ADP
ejpam-5300	4	26	foundational	foundational	ADJ
ejpam-5300	4	27	mathematical	mathematical	ADJ
ejpam-5300	4	28	tools	tool	NOUN
ejpam-5300	4	29	,	,	PUNCT
ejpam-5300	4	30	including	include	VERB
ejpam-5300	4	31	mathematical	mathematical	ADJ
ejpam-5300	4	32	induction	induction	NOUN
ejpam-5300	4	33	,	,	PUNCT
ejpam-5300	4	34	heron	heron	NOUN
ejpam-5300	4	35	’s	’s	PART
ejpam-5300	4	36	formula	formula	NOUN
ejpam-5300	4	37	,	,	PUNCT
ejpam-5300	4	38	and	and	CCONJ
ejpam-5300	4	39	the	the	DET
ejpam-5300	4	40	telescoping	telescope	VERB
ejpam-5300	4	41	product	product	NOUN
ejpam-5300	4	42	.	.	PUNCT
ejpam-5300	5	1	a	a	DET
ejpam-5300	5	2	generalized	generalized	ADJ
ejpam-5300	5	3	equation	equation	NOUN
ejpam-5300	5	4	for	for	ADP
ejpam-5300	5	5	n	n	DET
ejpam-5300	5	6	circles	circle	NOUN
ejpam-5300	5	7	based	base	VERB
ejpam-5300	5	8	on	on	ADP
ejpam-5300	5	9	the	the	DET
ejpam-5300	5	10	equal	equal	ADJ
ejpam-5300	5	11	incircles	incircle	NOUN
ejpam-5300	5	12	theorem	theorem	NOUN
ejpam-5300	5	13	is	be	AUX
ejpam-5300	5	14	derived	derive	VERB
ejpam-5300	5	15	through	through	ADP
ejpam-5300	5	16	explicit	explicit	ADJ
ejpam-5300	5	17	mathematical	mathematical	ADJ
ejpam-5300	5	18	formulation	formulation	NOUN
ejpam-5300	5	19	and	and	CCONJ
ejpam-5300	5	20	characterization	characterization	NOUN
ejpam-5300	5	21	.	.	PUNCT
ejpam-5300	6	1	the	the	DET
ejpam-5300	6	2	findings	finding	NOUN
ejpam-5300	6	3	deepen	deepen	VERB
ejpam-5300	6	4	our	our	PRON
ejpam-5300	6	5	understanding	understanding	NOUN
ejpam-5300	6	6	of	of	ADP
ejpam-5300	6	7	geometric	geometric	ADJ
ejpam-5300	6	8	relationships	relationship	NOUN
ejpam-5300	6	9	,	,	PUNCT
ejpam-5300	6	10	highlight	highlight	VERB
ejpam-5300	6	11	the	the	DET
ejpam-5300	6	12	historical	historical	ADJ
ejpam-5300	6	13	significance	significance	NOUN
ejpam-5300	6	14	of	of	ADP
ejpam-5300	6	15	sangaku	sangaku	NOUN
ejpam-5300	6	16	problems	problem	NOUN
ejpam-5300	6	17	,	,	PUNCT
ejpam-5300	6	18	and	and	CCONJ
ejpam-5300	6	19	offer	offer	VERB
ejpam-5300	6	20	potential	potential	ADJ
ejpam-5300	6	21	advancements	advancement	NOUN
ejpam-5300	6	22	for	for	ADP
ejpam-5300	6	23	future	future	ADJ
ejpam-5300	6	24	engineering	engineering	NOUN
ejpam-5300	6	25	applications	application	NOUN
ejpam-5300	6	26	,	,	PUNCT
ejpam-5300	6	27	mathematics	mathematic	NOUN
ejpam-5300	6	28	education	education	NOUN
ejpam-5300	6	29	,	,	PUNCT
ejpam-5300	6	30	and	and	CCONJ
ejpam-5300	6	31	research	research	NOUN
ejpam-5300	6	32	in	in	ADP
ejpam-5300	6	33	mathematical	mathematical	ADJ
ejpam-5300	6	34	history	history	NOUN
ejpam-5300	6	35	.	.	PUNCT
ejpam-5300	7	1	2020	2020	NUM
ejpam-5300	7	2	mathematics	mathematic	NOUN
ejpam-5300	7	3	subject	subject	NOUN
ejpam-5300	7	4	classifications	classification	NOUN
ejpam-5300	7	5	:	:	PUNCT
ejpam-5300	7	6	51m04	51m04	NUM
ejpam-5300	7	7	,	,	PUNCT
ejpam-5300	7	8	01a27	01a27	X
ejpam-5300	7	9	key	key	ADJ
ejpam-5300	7	10	words	word	NOUN
ejpam-5300	7	11	and	and	CCONJ
ejpam-5300	7	12	phrases	phrase	NOUN
ejpam-5300	7	13	:	:	PUNCT
ejpam-5300	7	14	sangaku	sangaku	NOUN
ejpam-5300	7	15	problems	problem	NOUN
ejpam-5300	7	16	,	,	PUNCT
ejpam-5300	7	17	equal	equal	ADJ
ejpam-5300	7	18	incircle	incircle	NOUN
ejpam-5300	7	19	theorem	theorem	PROPN
ejpam-5300	7	20	,	,	PUNCT
ejpam-5300	7	21	angela	angela	PROPN
ejpam-5300	7	22	drei	drei	PROPN
ejpam-5300	7	23	’s	’s	PART
ejpam-5300	7	24	proof	proof	NOUN
ejpam-5300	7	25	1	1	NUM
ejpam-5300	7	26	.	.	PUNCT
ejpam-5300	8	1	introduction	introduction	NOUN
ejpam-5300	8	2	sangaku	sangaku	NOUN
ejpam-5300	8	3	are	be	AUX
ejpam-5300	8	4	wooden	wooden	ADJ
ejpam-5300	8	5	tablets	tablet	NOUN
ejpam-5300	8	6	inscribed	inscribe	VERB
ejpam-5300	8	7	with	with	ADP
ejpam-5300	8	8	various	various	ADJ
ejpam-5300	8	9	geometrical	geometrical	ADJ
ejpam-5300	8	10	problems	problem	NOUN
ejpam-5300	8	11	and	and	CCONJ
ejpam-5300	8	12	devoted	devote	VERB
ejpam-5300	8	13	to	to	PART
ejpam-5300	8	14	shinto	shinto	VERB
ejpam-5300	8	15	shrines	shrine	NOUN
ejpam-5300	8	16	and	and	CCONJ
ejpam-5300	8	17	buddhist	buddhist	ADJ
ejpam-5300	8	18	temples	temple	NOUN
ejpam-5300	8	19	,	,	PUNCT
ejpam-5300	8	20	as	as	SCONJ
ejpam-5300	8	21	shown	show	VERB
ejpam-5300	8	22	in	in	ADP
ejpam-5300	8	23	figure	figure	NOUN
ejpam-5300	8	24	1	1	NUM
ejpam-5300	8	25	,	,	PUNCT
ejpam-5300	8	26	during	during	ADP
ejpam-5300	8	27	the	the	DET
ejpam-5300	8	28	japanese	japanese	ADJ
ejpam-5300	8	29	edo	edo	PROPN
ejpam-5300	8	30	period	period	NOUN
ejpam-5300	8	31	(	(	PUNCT
ejpam-5300	8	32	1603	1603	NUM
ejpam-5300	8	33	-	-	SYM
ejpam-5300	8	34	1868	1868	NUM
ejpam-5300	8	35	ce	ce	PROPN
ejpam-5300	8	36	)	)	PUNCT
ejpam-5300	8	37	this	this	PRON
ejpam-5300	8	38	is	be	AUX
ejpam-5300	8	39	a	a	DET
ejpam-5300	8	40	book	book	NOUN
ejpam-5300	8	41	:	:	PUNCT
ejpam-5300	8	42	[	[	X
ejpam-5300	8	43	2	2	NUM
ejpam-5300	8	44	]	]	PUNCT
ejpam-5300	8	45	.	.	PUNCT
ejpam-5300	9	1	the	the	DET
ejpam-5300	9	2	historical	historical	ADJ
ejpam-5300	9	3	significance	significance	NOUN
ejpam-5300	9	4	of	of	ADP
ejpam-5300	9	5	this	this	DET
ejpam-5300	9	6	tradition	tradition	NOUN
ejpam-5300	9	7	was	be	AUX
ejpam-5300	9	8	largely	largely	ADV
ejpam-5300	9	9	unrecognized	unrecognize	VERB
ejpam-5300	9	10	by	by	ADP
ejpam-5300	9	11	scholars	scholar	NOUN
ejpam-5300	9	12	until	until	SCONJ
ejpam-5300	9	13	it	it	PRON
ejpam-5300	9	14	was	be	AUX
ejpam-5300	9	15	brought	bring	VERB
ejpam-5300	9	16	to	to	ADP
ejpam-5300	9	17	light	light	NOUN
ejpam-5300	9	18	through	through	ADP
ejpam-5300	9	19	the	the	DET
ejpam-5300	9	20	publication	publication	NOUN
ejpam-5300	9	21	japanese	japanese	ADJ
ejpam-5300	9	22	temple	temple	PROPN
ejpam-5300	9	23	problems	problem	NOUN
ejpam-5300	9	24	:	:	PUNCT
ejpam-5300	9	25	sangaku	sangaku	PROPN
ejpam-5300	9	26	.	.	PUNCT
ejpam-5300	10	1	this	this	DET
ejpam-5300	10	2	source	source	NOUN
ejpam-5300	10	3	discovered	discover	VERB
ejpam-5300	10	4	by	by	ADP
ejpam-5300	10	5	an	an	DET
ejpam-5300	10	6	article	article	NOUN
ejpam-5300	10	7	in	in	ADP
ejpam-5300	10	8	a	a	DET
ejpam-5300	10	9	collection	collection	NOUN
ejpam-5300	10	10	:	:	PUNCT
ejpam-5300	10	11	[	[	X
ejpam-5300	10	12	5	5	X
ejpam-5300	10	13	]	]	PUNCT
ejpam-5300	10	14	notes	note	VERB
ejpam-5300	10	15	that	that	SCONJ
ejpam-5300	10	16	japanese	japanese	ADJ
ejpam-5300	10	17	temple	temple	PROPN
ejpam-5300	10	18	geometry	geometry	NOUN
ejpam-5300	10	19	often	often	ADV
ejpam-5300	10	20	predated	predate	VERB
ejpam-5300	10	21	the	the	DET
ejpam-5300	10	22	discovery	discovery	NOUN
ejpam-5300	10	23	of	of	ADP
ejpam-5300	10	24	several	several	ADJ
ejpam-5300	10	25	well	well	ADV
ejpam-5300	10	26	-	-	PUNCT
ejpam-5300	10	27	known	know	VERB
ejpam-5300	10	28	western	western	ADJ
ejpam-5300	10	29	geometric	geometric	ADJ
ejpam-5300	10	30	theorems	theorem	NOUN
ejpam-5300	10	31	,	,	PUNCT
ejpam-5300	10	32	such	such	ADJ
ejpam-5300	10	33	as	as	ADP
ejpam-5300	10	34	the	the	DET
ejpam-5300	10	35	katayamahiko	katayamahiko	NOUN
ejpam-5300	10	36	temple	temple	PROPN
ejpam-5300	10	37	problem	problem	NOUN
ejpam-5300	10	38	,	,	PUNCT
ejpam-5300	10	39	meiserinji	meiserinji	PROPN
ejpam-5300	10	40	temple	temple	PROPN
ejpam-5300	10	41	problem	problem	NOUN
ejpam-5300	10	42	,	,	PUNCT
ejpam-5300	10	43	and	and	CCONJ
ejpam-5300	10	44	the	the	DET
ejpam-5300	10	45	equal	equal	ADJ
ejpam-5300	10	46	incircles	incircle	NOUN
ejpam-5300	10	47	theorem	theorem	VERB
ejpam-5300	10	48	.	.	PUNCT
ejpam-5300	11	1	subsequently	subsequently	ADV
ejpam-5300	11	2	,	,	PUNCT
ejpam-5300	11	3	the	the	DET
ejpam-5300	11	4	geometrical	geometrical	ADJ
ejpam-5300	11	5	principles	principle	NOUN
ejpam-5300	11	6	underlying	underlie	VERB
ejpam-5300	11	7	japanese	japanese	ADJ
ejpam-5300	11	8	temple	temple	NOUN
ejpam-5300	11	9	architecture	architecture	NOUN
ejpam-5300	11	10	were	be	AUX
ejpam-5300	11	11	documented	document	VERB
ejpam-5300	11	12	in	in	ADP
ejpam-5300	11	13	the	the	DET
ejpam-5300	11	14	book	book	NOUN
ejpam-5300	11	15	sacred	sacred	ADJ
ejpam-5300	11	16	mathematics	mathematic	NOUN
ejpam-5300	11	17	:	:	PUNCT
ejpam-5300	11	18	japanese	japanese	ADJ
ejpam-5300	11	19	temple	temple	PROPN
ejpam-5300	11	20	geometry	geometry	NOUN
ejpam-5300	11	21	this	this	PRON
ejpam-5300	11	22	is	be	AUX
ejpam-5300	11	23	a	a	DET
ejpam-5300	11	24	book	book	NOUN
ejpam-5300	11	25	:	:	PUNCT
ejpam-5300	11	26	[	[	X
ejpam-5300	11	27	4	4	NUM
ejpam-5300	11	28	]	]	PUNCT
ejpam-5300	11	29	.	.	PUNCT
ejpam-5300	12	1	following	follow	VERB
ejpam-5300	12	2	this	this	PRON
ejpam-5300	12	3	,	,	PUNCT
ejpam-5300	12	4	an	an	DET
ejpam-5300	12	5	investigation	investigation	NOUN
ejpam-5300	12	6	led	lead	VERB
ejpam-5300	12	7	by	by	ADP
ejpam-5300	12	8	r.	r.	PROPN
ejpam-5300	12	9	j.	j.	PROPN
ejpam-5300	12	10	hosking	hosking	PROPN
ejpam-5300	12	11	[	[	AUX
ejpam-5300	12	12	see	see	VERB
ejpam-5300	12	13	also	also	ADV
ejpam-5300	12	14	[	[	X
ejpam-5300	12	15	7	7	NUM
ejpam-5300	12	16	]	]	X
ejpam-5300	12	17	]	]	X
ejpam-5300	12	18	as	as	ADP
ejpam-5300	12	19	a	a	DET
ejpam-5300	12	20	technical	technical	ADJ
ejpam-5300	12	21	report	report	NOUN
ejpam-5300	12	22	,	,	PUNCT
ejpam-5300	12	23	addressed	address	VERB
ejpam-5300	12	24	a	a	DET
ejpam-5300	12	25	traditional	traditional	ADJ
ejpam-5300	12	26	mathematical	mathematical	ADJ
ejpam-5300	12	27	approach	approach	NOUN
ejpam-5300	12	28	to	to	ADP
ejpam-5300	12	29	a	a	DET
ejpam-5300	12	30	sangaku	sangaku	NOUN
ejpam-5300	12	31	problem	problem	NOUN
ejpam-5300	12	32	from	from	ADP
ejpam-5300	12	33	okayama	okayama	PROPN
ejpam-5300	12	34	prefecture	prefecture	NOUN
ejpam-5300	12	35	,	,	PUNCT
ejpam-5300	12	36	as	as	SCONJ
ejpam-5300	12	37	shown	show	VERB
ejpam-5300	12	38	in	in	ADP
ejpam-5300	12	39	figure	figure	NOUN
ejpam-5300	12	40	2	2	NUM
ejpam-5300	12	41	.	.	PUNCT
ejpam-5300	13	1	however	however	ADV
ejpam-5300	13	2	,	,	PUNCT
ejpam-5300	13	3	these	these	DET
ejpam-5300	13	4	sangaku	sangaku	NOUN
ejpam-5300	13	5	problems	problem	NOUN
ejpam-5300	13	6	still	still	ADV
ejpam-5300	13	7	lack	lack	VERB
ejpam-5300	13	8	modern	modern	ADJ
ejpam-5300	13	9	alternative	alternative	ADJ
ejpam-5300	13	10	mathematical	mathematical	ADJ
ejpam-5300	13	11	methods	method	NOUN
ejpam-5300	13	12	to	to	PART
ejpam-5300	13	13	gain	gain	VERB
ejpam-5300	13	14	deeper	deep	ADJ
ejpam-5300	13	15	insights	insight	NOUN
ejpam-5300	13	16	.	.	PUNCT
ejpam-5300	14	1	recent	recent	ADJ
ejpam-5300	14	2	investigations	investigation	NOUN
ejpam-5300	14	3	have	have	AUX
ejpam-5300	14	4	reported	report	VERB
ejpam-5300	14	5	that	that	SCONJ
ejpam-5300	14	6	these	these	DET
ejpam-5300	14	7	ancient	ancient	ADJ
ejpam-5300	14	8	problems	problem	NOUN
ejpam-5300	14	9	have	have	AUX
ejpam-5300	14	10	contributed	contribute	VERB
ejpam-5300	14	11	to	to	ADP
ejpam-5300	14	12	modern	modern	ADJ
ejpam-5300	14	13	mathematical	mathematical	ADJ
ejpam-5300	14	14	methods	method	NOUN
ejpam-5300	14	15	,	,	PUNCT
ejpam-5300	14	16	particularly	particularly	ADV
ejpam-5300	14	17	in	in	ADP
ejpam-5300	14	18	the	the	DET
ejpam-5300	14	19	field	field	NOUN
ejpam-5300	14	20	of	of	ADP
ejpam-5300	14	21	discrete	discrete	ADJ
ejpam-5300	14	22	geometry	geometry	NOUN
ejpam-5300	14	23	.	.	PUNCT
ejpam-5300	15	1	notable	notable	ADJ
ejpam-5300	15	2	examples	example	NOUN
ejpam-5300	15	3	include	include	VERB
ejpam-5300	15	4	the	the	DET
ejpam-5300	15	5	geometric	geometric	ADJ
ejpam-5300	15	6	inversion	inversion	NOUN
ejpam-5300	15	7	method	method	NOUN
ejpam-5300	15	8	[	[	AUX
ejpam-5300	15	9	see	see	VERB
ejpam-5300	15	10	also	also	ADV
ejpam-5300	15	11	[	[	X
ejpam-5300	15	12	10	10	NUM
ejpam-5300	15	13	]	]	X
ejpam-5300	15	14	]	]	X
ejpam-5300	15	15	a	a	DET
ejpam-5300	15	16	journal	journal	NOUN
ejpam-5300	15	17	article	article	NOUN
ejpam-5300	15	18	,	,	PUNCT
ejpam-5300	15	19	euclidean	euclidean	ADJ
ejpam-5300	15	20	geometry	geometry	NOUN
ejpam-5300	15	21	[	[	X
ejpam-5300	15	22	see	see	VERB
ejpam-5300	15	23	also	also	ADV
ejpam-5300	15	24	[	[	X
ejpam-5300	15	25	6	6	NUM
ejpam-5300	15	26	]	]	X
ejpam-5300	15	27	]	]	X
ejpam-5300	15	28	a	a	DET
ejpam-5300	15	29	journal	journal	NOUN
ejpam-5300	15	30	article	article	NOUN
ejpam-5300	15	31	,	,	PUNCT
ejpam-5300	15	32	and	and	CCONJ
ejpam-5300	15	33	so	so	ADV
ejpam-5300	15	34	on	on	ADV
ejpam-5300	15	35	.	.	PUNCT
ejpam-5300	16	1	doi	doi	NOUN
ejpam-5300	16	2	:	:	PUNCT
ejpam-5300	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5300	https://doi.org/10.29020/nybg.ejpam.v17i4.5300	DET
ejpam-5300	16	4	email	email	NOUN
ejpam-5300	16	5	address	address	NOUN
ejpam-5300	16	6	:	:	PUNCT
ejpam-5300	16	7	perawit.boon@mail.kmutt.ac.th	perawit.boon@mail.kmutt.ac.th	PROPN
ejpam-5300	16	8	(	(	PUNCT
ejpam-5300	16	9	p.	p.	NOUN
ejpam-5300	16	10	boonsomchua	boonsomchua	PROPN
ejpam-5300	16	11	)	)	PUNCT
ejpam-5300	16	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5300	16	13	4135	4135	NUM
ejpam-5300	16	14	copyright	copyright	NOUN
ejpam-5300	16	15	:	:	PUNCT
ejpam-5300	16	16	©	©	PROPN
ejpam-5300	16	17	2024	2024	NUM
ejpam-5300	16	18	the	the	DET
ejpam-5300	16	19	author(s	author(s	NOUN
ejpam-5300	16	20	)	)	PUNCT
ejpam-5300	16	21	.	.	PUNCT
ejpam-5300	17	1	(	(	PUNCT
ejpam-5300	17	2	cc	cc	NOUN
ejpam-5300	17	3	by	by	ADP
ejpam-5300	17	4	-	-	PUNCT
ejpam-5300	17	5	nc	nc	PROPN
ejpam-5300	17	6	4.0	4.0	NUM
ejpam-5300	17	7	)	)	PUNCT
ejpam-5300	17	8	p.	p.	NOUN
ejpam-5300	17	9	boonsomchua	boonsomchua	PROPN
ejpam-5300	17	10	/	/	SYM
ejpam-5300	17	11	eur	eur	PROPN
ejpam-5300	17	12	.	.	PUNCT
ejpam-5300	18	1	j.	j.	PROPN
ejpam-5300	18	2	pure	pure	PROPN
ejpam-5300	18	3	appl	appl	PROPN
ejpam-5300	18	4	.	.	PROPN
ejpam-5300	18	5	math	math	PROPN
ejpam-5300	18	6	,	,	PUNCT
ejpam-5300	18	7	17	17	NUM
ejpam-5300	18	8	(	(	PUNCT
ejpam-5300	18	9	4	4	NUM
ejpam-5300	18	10	)	)	PUNCT
ejpam-5300	18	11	(	(	PUNCT
ejpam-5300	18	12	2024	2024	NUM
ejpam-5300	18	13	)	)	PUNCT
ejpam-5300	18	14	,	,	PUNCT
ejpam-5300	18	15	4135	4135	NUM
ejpam-5300	18	16	-	-	SYM
ejpam-5300	18	17	4146	4146	NUM
ejpam-5300	18	18	4136	4136	NUM
ejpam-5300	18	19	figure	figure	NOUN
ejpam-5300	18	20	1	1	NUM
ejpam-5300	18	21	:	:	PUNCT
ejpam-5300	18	22	a	a	DET
ejpam-5300	18	23	sangaku	sangaku	NOUN
ejpam-5300	18	24	board	board	NOUN
ejpam-5300	18	25	hanging	hang	VERB
ejpam-5300	18	26	under	under	ADP
ejpam-5300	18	27	the	the	DET
ejpam-5300	18	28	roof	roof	NOUN
ejpam-5300	18	29	of	of	ADP
ejpam-5300	18	30	a	a	DET
ejpam-5300	18	31	temple	temple	NOUN
ejpam-5300	18	32	in	in	ADP
ejpam-5300	18	33	japan	japan	PROPN
ejpam-5300	18	34	.	.	PUNCT
ejpam-5300	19	1	figure	figure	VERB
ejpam-5300	19	2	2	2	NUM
ejpam-5300	19	3	:	:	PUNCT
ejpam-5300	19	4	sangaku	sangaku	NOUN
ejpam-5300	19	5	problems	problem	NOUN
ejpam-5300	19	6	at	at	ADP
ejpam-5300	19	7	katayamahiko	katayamahiko	PROPN
ejpam-5300	19	8	shrine	shrine	PROPN
ejpam-5300	19	9	.	.	PUNCT
ejpam-5300	20	1	equal	equal	ADJ
ejpam-5300	20	2	incircles	incircle	NOUN
ejpam-5300	20	3	theorem	theorem	NOUN
ejpam-5300	20	4	let	let	VERB
ejpam-5300	20	5	c	c	PRON
ejpam-5300	20	6	be	be	AUX
ejpam-5300	20	7	a	a	DET
ejpam-5300	20	8	point	point	NOUN
ejpam-5300	20	9	.	.	PUNCT
ejpam-5300	21	1	assume	assume	VERB
ejpam-5300	21	2	points	point	NOUN
ejpam-5300	21	3	mi	mi	PROPN
ejpam-5300	21	4	,	,	PUNCT
ejpam-5300	21	5	for	for	ADP
ejpam-5300	21	6	i	i	PROPN
ejpam-5300	21	7	=	=	SYM
ejpam-5300	21	8	1	1	NUM
ejpam-5300	21	9	,	,	PUNCT
ejpam-5300	21	10	2	2	NUM
ejpam-5300	21	11	,	,	PUNCT
ejpam-5300	21	12	.	.	PUNCT
ejpam-5300	21	13	.	.	PUNCT
ejpam-5300	22	1	.	.	PUNCT
ejpam-5300	23	1	,	,	PUNCT
ejpam-5300	23	2	n	n	X
ejpam-5300	23	3	(	(	PUNCT
ejpam-5300	23	4	n	n	X
ejpam-5300	23	5	>	>	X
ejpam-5300	23	6	3	3	NUM
ejpam-5300	23	7	)	)	PUNCT
ejpam-5300	23	8	,	,	PUNCT
ejpam-5300	23	9	lie	lie	VERB
ejpam-5300	23	10	on	on	ADP
ejpam-5300	23	11	a	a	DET
ejpam-5300	23	12	line	line	NOUN
ejpam-5300	23	13	not	not	PART
ejpam-5300	23	14	passing	pass	VERB
ejpam-5300	23	15	through	through	ADP
ejpam-5300	23	16	c.	c.	PROPN
ejpam-5300	23	17	assume	assume	VERB
ejpam-5300	23	18	further	far	ADV
ejpam-5300	23	19	that	that	SCONJ
ejpam-5300	23	20	the	the	DET
ejpam-5300	23	21	incircles	incircle	NOUN
ejpam-5300	23	22	of	of	ADP
ejpam-5300	23	23	triangles	triangle	NOUN
ejpam-5300	23	24	m1cm2	m1cm2	NOUN
ejpam-5300	23	25	,	,	PUNCT
ejpam-5300	23	26	m2cm3	m2cm3	NOUN
ejpam-5300	23	27	,	,	PUNCT
ejpam-5300	23	28	.	.	PUNCT
ejpam-5300	23	29	.	.	PUNCT
ejpam-5300	24	1	.	.	PUNCT
ejpam-5300	25	1	,	,	PUNCT
ejpam-5300	25	2	mn−1cmn	mn−1cmn	NOUN
ejpam-5300	25	3	all	all	PRON
ejpam-5300	25	4	have	have	VERB
ejpam-5300	25	5	equal	equal	ADJ
ejpam-5300	25	6	radii	radius	NOUN
ejpam-5300	25	7	.	.	PUNCT
ejpam-5300	26	1	then	then	ADV
ejpam-5300	26	2	the	the	DET
ejpam-5300	26	3	same	same	ADJ
ejpam-5300	26	4	is	be	AUX
ejpam-5300	26	5	true	true	ADJ
ejpam-5300	26	6	for	for	ADP
ejpam-5300	26	7	the	the	DET
ejpam-5300	26	8	triangles	triangle	NOUN
ejpam-5300	26	9	m1cm3	m1cm3	PROPN
ejpam-5300	26	10	,	,	PUNCT
ejpam-5300	26	11	m2cm4	m2cm4	NOUN
ejpam-5300	26	12	,	,	PUNCT
ejpam-5300	26	13	.	.	PUNCT
ejpam-5300	26	14	.	.	PUNCT
ejpam-5300	27	1	.	.	PUNCT
ejpam-5300	28	1	,	,	PUNCT
ejpam-5300	28	2	mn−2cmn	mn−2cmn	NOUN
ejpam-5300	28	3	,	,	PUNCT
ejpam-5300	28	4	and	and	CCONJ
ejpam-5300	28	5	also	also	ADV
ejpam-5300	28	6	for	for	ADP
ejpam-5300	28	7	the	the	DET
ejpam-5300	28	8	triangles	triangle	NOUN
ejpam-5300	28	9	m1cm4	m1cm4	NOUN
ejpam-5300	28	10	,	,	PUNCT
ejpam-5300	28	11	m2cm5	m2cm5	ADJ
ejpam-5300	28	12	,	,	PUNCT
ejpam-5300	28	13	.	.	PUNCT
ejpam-5300	28	14	.	.	PUNCT
ejpam-5300	29	1	.	.	PUNCT
ejpam-5300	30	1	,	,	PUNCT
ejpam-5300	30	2	mn−3cmn	mn−3cmn	NOUN
ejpam-5300	30	3	,	,	PUNCT
ejpam-5300	30	4	and	and	CCONJ
ejpam-5300	30	5	so	so	ADV
ejpam-5300	30	6	on	on	ADV
ejpam-5300	30	7	.	.	PUNCT
ejpam-5300	31	1	figure	figure	VERB
ejpam-5300	31	2	3	3	NUM
ejpam-5300	31	3	:	:	PUNCT
ejpam-5300	31	4	the	the	DET
ejpam-5300	31	5	image	image	NOUN
ejpam-5300	31	6	depicts	depict	VERB
ejpam-5300	31	7	the	the	DET
ejpam-5300	31	8	diagram	diagram	NOUN
ejpam-5300	31	9	associated	associate	VERB
ejpam-5300	31	10	with	with	ADP
ejpam-5300	31	11	the	the	DET
ejpam-5300	31	12	equal	equal	ADJ
ejpam-5300	31	13	incircles	incircle	NOUN
ejpam-5300	31	14	theorem	theorem	VERB
ejpam-5300	31	15	.	.	PUNCT
ejpam-5300	32	1	several	several	ADJ
ejpam-5300	32	2	sangaku	sangaku	NOUN
ejpam-5300	32	3	problems	problem	NOUN
ejpam-5300	32	4	from	from	ADP
ejpam-5300	32	5	japan	japan	PROPN
ejpam-5300	32	6	remain	remain	VERB
ejpam-5300	32	7	unsolved	unsolved	ADJ
ejpam-5300	32	8	or	or	CCONJ
ejpam-5300	32	9	lack	lack	NOUN
ejpam-5300	32	10	characterization	characterization	NOUN
ejpam-5300	32	11	in	in	ADP
ejpam-5300	32	12	mathematical	mathematical	ADJ
ejpam-5300	32	13	theorems	theorem	NOUN
ejpam-5300	32	14	that	that	PRON
ejpam-5300	32	15	used	use	VERB
ejpam-5300	32	16	to	to	PART
ejpam-5300	32	17	explicit	explicit	ADJ
ejpam-5300	32	18	mathematical	mathematical	ADJ
ejpam-5300	32	19	formulations	formulation	NOUN
ejpam-5300	32	20	,	,	PUNCT
ejpam-5300	32	21	including	include	VERB
ejpam-5300	32	22	the	the	DET
ejpam-5300	32	23	“	"	PUNCT
ejpam-5300	32	24	equal	equal	ADJ
ejpam-5300	32	25	incircle	incircle	NOUN
ejpam-5300	32	26	theorem	theorem	VERB
ejpam-5300	32	27	”	"	PUNCT
ejpam-5300	32	28	[	[	X
ejpam-5300	32	29	see	see	VERB
ejpam-5300	32	30	also	also	ADV
ejpam-5300	32	31	[	[	X
ejpam-5300	32	32	3	3	NUM
ejpam-5300	32	33	]	]	PUNCT
ejpam-5300	32	34	]	]	PUNCT
ejpam-5300	32	35	as	as	ADP
ejpam-5300	32	36	technical	technical	ADJ
ejpam-5300	32	37	reports	report	NOUN
ejpam-5300	32	38	,	,	PUNCT
ejpam-5300	32	39	which	which	PRON
ejpam-5300	32	40	presents	present	VERB
ejpam-5300	32	41	a	a	DET
ejpam-5300	32	42	configuration	configuration	NOUN
ejpam-5300	32	43	of	of	ADP
ejpam-5300	32	44	multiple	multiple	ADJ
ejpam-5300	32	45	equal	equal	ADJ
ejpam-5300	32	46	circles	circle	NOUN
ejpam-5300	32	47	inscribed	inscribe	VERB
ejpam-5300	32	48	within	within	ADP
ejpam-5300	32	49	the	the	DET
ejpam-5300	32	50	same	same	ADJ
ejpam-5300	32	51	number	number	NOUN
ejpam-5300	32	52	of	of	ADP
ejpam-5300	32	53	sub	sub	NOUN
ejpam-5300	32	54	-	-	NOUN
ejpam-5300	32	55	triangles	triangle	NOUN
ejpam-5300	32	56	,	,	PUNCT
ejpam-5300	32	57	with	with	ADP
ejpam-5300	32	58	larger	large	ADJ
ejpam-5300	32	59	equal	equal	ADJ
ejpam-5300	32	60	circles	circle	NOUN
ejpam-5300	32	61	inscribed	inscribe	VERB
ejpam-5300	32	62	within	within	ADP
ejpam-5300	32	63	the	the	DET
ejpam-5300	32	64	larger	large	ADJ
ejpam-5300	32	65	triangles	triangle	NOUN
ejpam-5300	32	66	,	,	PUNCT
ejpam-5300	32	67	as	as	SCONJ
ejpam-5300	32	68	shown	show	VERB
ejpam-5300	32	69	in	in	ADP
ejpam-5300	32	70	figure	figure	NOUN
ejpam-5300	32	71	3	3	NUM
ejpam-5300	32	72	.	.	PUNCT
ejpam-5300	32	73	subsequently	subsequently	ADV
ejpam-5300	32	74	,	,	PUNCT
ejpam-5300	32	75	angela	angela	PROPN
ejpam-5300	32	76	drei	drei	PROPN
ejpam-5300	32	77	’s	’s	PART
ejpam-5300	32	78	proof	proof	NOUN
ejpam-5300	32	79	provides	provide	VERB
ejpam-5300	32	80	initial	initial	ADJ
ejpam-5300	32	81	mathematical	mathematical	ADJ
ejpam-5300	32	82	formulations	formulation	NOUN
ejpam-5300	32	83	for	for	ADP
ejpam-5300	32	84	two	two	NUM
ejpam-5300	32	85	sangaku	sangaku	NOUN
ejpam-5300	32	86	problems	problem	NOUN
ejpam-5300	32	87	with	with	ADP
ejpam-5300	32	88	equal	equal	ADJ
ejpam-5300	32	89	incircles	incircle	NOUN
ejpam-5300	32	90	,	,	PUNCT
ejpam-5300	32	91	employed	employ	VERB
ejpam-5300	32	92	to	to	PART
ejpam-5300	32	93	characterize	characterize	VERB
ejpam-5300	32	94	the	the	DET
ejpam-5300	32	95	geometrical	geometrical	ADJ
ejpam-5300	32	96	relationships	relationship	NOUN
ejpam-5300	32	97	expressed	express	VERB
ejpam-5300	32	98	in	in	ADP
ejpam-5300	32	99	terms	term	NOUN
ejpam-5300	32	100	of	of	ADP
ejpam-5300	32	101	trigonometric	trigonometric	ADJ
ejpam-5300	32	102	forms	form	NOUN
ejpam-5300	32	103	.	.	PUNCT
ejpam-5300	33	1	so	so	ADV
ejpam-5300	33	2	,	,	PUNCT
ejpam-5300	33	3	this	this	DET
ejpam-5300	33	4	paper	paper	NOUN
ejpam-5300	33	5	aims	aim	VERB
ejpam-5300	33	6	to	to	PART
ejpam-5300	33	7	develop	develop	VERB
ejpam-5300	33	8	a	a	DET
ejpam-5300	33	9	mathematical	mathematical	ADJ
ejpam-5300	33	10	framework	framework	NOUN
ejpam-5300	33	11	that	that	PRON
ejpam-5300	33	12	generalizes	generalize	VERB
ejpam-5300	33	13	the	the	DET
ejpam-5300	33	14	multiple	multiple	ADJ
ejpam-5300	33	15	incircles	incircle	NOUN
ejpam-5300	33	16	problem	problem	NOUN
ejpam-5300	33	17	,	,	PUNCT
ejpam-5300	33	18	enabling	enable	VERB
ejpam-5300	33	19	non	non	ADJ
ejpam-5300	33	20	-	-	ADJ
ejpam-5300	33	21	equal	equal	ADJ
ejpam-5300	33	22	radii	radius	NOUN
ejpam-5300	33	23	,	,	PUNCT
ejpam-5300	33	24	by	by	ADP
ejpam-5300	33	25	extending	extend	VERB
ejpam-5300	33	26	from	from	ADP
ejpam-5300	33	27	the	the	DET
ejpam-5300	33	28	equal	equal	ADJ
ejpam-5300	33	29	incircles	incircle	NOUN
ejpam-5300	33	30	theorem	theorem	VERB
ejpam-5300	33	31	.	.	PUNCT
ejpam-5300	34	1	the	the	DET
ejpam-5300	34	2	study	study	NOUN
ejpam-5300	34	3	also	also	ADV
ejpam-5300	34	4	explores	explore	VERB
ejpam-5300	34	5	three	three	NUM
ejpam-5300	34	6	setups	setup	NOUN
ejpam-5300	34	7	:	:	PUNCT
ejpam-5300	34	8	(	(	PUNCT
ejpam-5300	34	9	1	1	X
ejpam-5300	34	10	)	)	PUNCT
ejpam-5300	34	11	two	two	NUM
ejpam-5300	34	12	tangent	tangent	ADJ
ejpam-5300	34	13	circles	circle	NOUN
ejpam-5300	34	14	within	within	ADP
ejpam-5300	34	15	a	a	DET
ejpam-5300	34	16	triangle	triangle	NOUN
ejpam-5300	34	17	in	in	ADP
ejpam-5300	34	18	section	section	NOUN
ejpam-5300	34	19	1	1	NUM
ejpam-5300	34	20	;	;	PUNCT
ejpam-5300	34	21	(	(	PUNCT
ejpam-5300	34	22	2	2	X
ejpam-5300	34	23	)	)	PUNCT
ejpam-5300	34	24	an	an	DET
ejpam-5300	34	25	analysis	analysis	NOUN
ejpam-5300	34	26	of	of	ADP
ejpam-5300	34	27	the	the	DET
ejpam-5300	34	28	inclusion	inclusion	NOUN
ejpam-5300	34	29	of	of	ADP
ejpam-5300	34	30	incircles	incircle	NOUN
ejpam-5300	34	31	in	in	ADP
ejpam-5300	34	32	a	a	DET
ejpam-5300	34	33	sectorial	sectorial	ADJ
ejpam-5300	34	34	triangular	triangular	NOUN
ejpam-5300	34	35	configuration	configuration	NOUN
ejpam-5300	34	36	in	in	ADP
ejpam-5300	34	37	section	section	NOUN
ejpam-5300	34	38	2	2	NUM
ejpam-5300	34	39	;	;	PUNCT
ejpam-5300	34	40	(	(	PUNCT
ejpam-5300	34	41	3	3	X
ejpam-5300	34	42	)	)	PUNCT
ejpam-5300	34	43	the	the	DET
ejpam-5300	34	44	analysis	analysis	NOUN
ejpam-5300	34	45	of	of	ADP
ejpam-5300	34	46	the	the	DET
ejpam-5300	34	47	inclusion	inclusion	NOUN
ejpam-5300	34	48	of	of	ADP
ejpam-5300	34	49	incircles	incircle	NOUN
ejpam-5300	34	50	and	and	CCONJ
ejpam-5300	34	51	ex	ex	NOUN
ejpam-5300	34	52	-	-	NOUN
ejpam-5300	34	53	circles	circle	NOUN
ejpam-5300	34	54	in	in	ADP
ejpam-5300	34	55	a	a	DET
ejpam-5300	34	56	sectorial	sectorial	ADJ
ejpam-5300	34	57	triangular	triangular	NOUN
ejpam-5300	34	58	configuration	configuration	NOUN
ejpam-5300	34	59	in	in	ADP
ejpam-5300	34	60	section	section	NOUN
ejpam-5300	34	61	3	3	NUM
ejpam-5300	34	62	.	.	PUNCT
ejpam-5300	35	1	p.	p.	NOUN
ejpam-5300	35	2	boonsomchua	boonsomchua	PROPN
ejpam-5300	35	3	/	/	SYM
ejpam-5300	35	4	eur	eur	PROPN
ejpam-5300	35	5	.	.	PUNCT
ejpam-5300	36	1	j.	j.	PROPN
ejpam-5300	36	2	pure	pure	PROPN
ejpam-5300	36	3	appl	appl	PROPN
ejpam-5300	36	4	.	.	PROPN
ejpam-5300	36	5	math	math	PROPN
ejpam-5300	36	6	,	,	PUNCT
ejpam-5300	36	7	17	17	NUM
ejpam-5300	36	8	(	(	PUNCT
ejpam-5300	36	9	4	4	NUM
ejpam-5300	36	10	)	)	PUNCT
ejpam-5300	36	11	(	(	PUNCT
ejpam-5300	36	12	2024	2024	NUM
ejpam-5300	36	13	)	)	PUNCT
ejpam-5300	36	14	,	,	PUNCT
ejpam-5300	36	15	4135	4135	NUM
ejpam-5300	36	16	-	-	SYM
ejpam-5300	36	17	4146	4146	NUM
ejpam-5300	36	18	4137	4137	NUM
ejpam-5300	36	19	2	2	NUM
ejpam-5300	36	20	.	.	X
ejpam-5300	36	21	main	main	ADJ
ejpam-5300	36	22	results	result	NOUN
ejpam-5300	36	23	this	this	DET
ejpam-5300	36	24	section	section	NOUN
ejpam-5300	36	25	has	have	AUX
ejpam-5300	36	26	formulated	formulate	VERB
ejpam-5300	36	27	an	an	DET
ejpam-5300	36	28	equation	equation	NOUN
ejpam-5300	36	29	that	that	PRON
ejpam-5300	36	30	describes	describes	AUX
ejpam-5300	36	31	generalized	generalize	VERB
ejpam-5300	36	32	adjacent	adjacent	ADJ
ejpam-5300	36	33	triangles	triangle	NOUN
ejpam-5300	36	34	with	with	ADP
ejpam-5300	36	35	inscribed	inscribe	VERB
ejpam-5300	36	36	circles	circle	NOUN
ejpam-5300	36	37	in	in	ADP
ejpam-5300	36	38	the	the	DET
ejpam-5300	36	39	initial	initial	ADJ
ejpam-5300	36	40	part	part	NOUN
ejpam-5300	36	41	and	and	CCONJ
ejpam-5300	36	42	ex	ex	NOUN
ejpam-5300	36	43	-	-	NOUN
ejpam-5300	36	44	circles	circle	NOUN
ejpam-5300	36	45	in	in	ADP
ejpam-5300	36	46	the	the	DET
ejpam-5300	36	47	remaining	remain	VERB
ejpam-5300	36	48	part	part	NOUN
ejpam-5300	36	49	,	,	PUNCT
ejpam-5300	36	50	based	base	VERB
ejpam-5300	36	51	on	on	ADP
ejpam-5300	36	52	angela	angela	PROPN
ejpam-5300	36	53	drei	drei	PROPN
ejpam-5300	36	54	’s	’s	PART
ejpam-5300	36	55	proof	proof	NOUN
ejpam-5300	36	56	.	.	PUNCT
ejpam-5300	37	1	this	this	DET
ejpam-5300	37	2	formulation	formulation	NOUN
ejpam-5300	37	3	is	be	AUX
ejpam-5300	37	4	extended	extend	VERB
ejpam-5300	37	5	to	to	ADP
ejpam-5300	37	6	other	other	ADJ
ejpam-5300	37	7	scenarios	scenario	NOUN
ejpam-5300	37	8	,	,	PUNCT
ejpam-5300	37	9	including	include	VERB
ejpam-5300	37	10	perpendicular	perpendicular	ADJ
ejpam-5300	37	11	and	and	CCONJ
ejpam-5300	37	12	angle	angle	NOUN
ejpam-5300	37	13	-	-	PUNCT
ejpam-5300	37	14	bisector	bisector	NOUN
ejpam-5300	37	15	cases	case	NOUN
ejpam-5300	37	16	.	.	PUNCT
ejpam-5300	38	1	section	section	NOUN
ejpam-5300	38	2	1	1	NUM
ejpam-5300	38	3	two	two	NUM
ejpam-5300	38	4	tangent	tangent	ADJ
ejpam-5300	38	5	circles	circle	NOUN
ejpam-5300	38	6	in	in	ADP
ejpam-5300	38	7	a	a	DET
ejpam-5300	38	8	triangle	triangle	NOUN
ejpam-5300	38	9	theorem	theorem	NOUN
ejpam-5300	38	10	1	1	NUM
ejpam-5300	38	11	let	let	VERB
ejpam-5300	38	12	a	a	DET
ejpam-5300	38	13	triangle	triangle	NOUN
ejpam-5300	38	14	△	△	X
ejpam-5300	38	15	ab1c1	ab1c1	X
ejpam-5300	38	16	with	with	ADP
ejpam-5300	38	17	vertices	vertex	NOUN
ejpam-5300	38	18	a	a	PRON
ejpam-5300	38	19	,	,	PUNCT
ejpam-5300	38	20	b1	b1	NOUN
ejpam-5300	38	21	,	,	PUNCT
ejpam-5300	38	22	and	and	CCONJ
ejpam-5300	38	23	c1	c1	PROPN
ejpam-5300	38	24	.	.	PUNCT
ejpam-5300	39	1	inside	inside	ADP
ejpam-5300	39	2	this	this	DET
ejpam-5300	39	3	triangle	triangle	NOUN
ejpam-5300	39	4	,	,	PUNCT
ejpam-5300	39	5	there	there	PRON
ejpam-5300	39	6	are	be	VERB
ejpam-5300	39	7	two	two	NUM
ejpam-5300	39	8	circles	circle	NOUN
ejpam-5300	39	9	.	.	PUNCT
ejpam-5300	40	1	let	let	VERB
ejpam-5300	40	2	circles	circle	NOUN
ejpam-5300	40	3	o1	o1	NOUN
ejpam-5300	40	4	(	(	PUNCT
ejpam-5300	40	5	green	green	ADJ
ejpam-5300	40	6	)	)	PUNCT
ejpam-5300	40	7	and	and	CCONJ
ejpam-5300	40	8	o2	o2	PROPN
ejpam-5300	40	9	(	(	PUNCT
ejpam-5300	40	10	blue	blue	ADJ
ejpam-5300	40	11	)	)	PUNCT
ejpam-5300	40	12	as	as	ADP
ejpam-5300	40	13	the	the	DET
ejpam-5300	40	14	incircles	incircle	NOUN
ejpam-5300	40	15	of	of	ADP
ejpam-5300	40	16	the	the	DET
ejpam-5300	40	17	triangles	triangle	NOUN
ejpam-5300	40	18	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	40	19	and	and	CCONJ
ejpam-5300	40	20	∆ac1b2	∆ac1b2	VERB
ejpam-5300	40	21	with	with	ADP
ejpam-5300	40	22	radii	radius	NOUN
ejpam-5300	40	23	r1	r1	NOUN
ejpam-5300	40	24	and	and	CCONJ
ejpam-5300	40	25	r2	r2	PROPN
ejpam-5300	40	26	respectively	respectively	ADV
ejpam-5300	40	27	.	.	PUNCT
ejpam-5300	41	1	circle	circle	PROPN
ejpam-5300	41	2	o1	o1	PROPN
ejpam-5300	41	3	is	be	AUX
ejpam-5300	41	4	tangent	tangent	NOUN
ejpam-5300	41	5	to	to	ADP
ejpam-5300	41	6	the	the	DET
ejpam-5300	41	7	sides	side	NOUN
ejpam-5300	41	8	ab1	ab1	ADV
ejpam-5300	41	9	,	,	PUNCT
ejpam-5300	41	10	ab2	ab2	NOUN
ejpam-5300	41	11	and	and	CCONJ
ejpam-5300	41	12	b1c1	b1c1	PROPN
ejpam-5300	41	13	at	at	ADP
ejpam-5300	41	14	points	point	NOUN
ejpam-5300	41	15	f1	f1	NOUN
ejpam-5300	41	16	,	,	PUNCT
ejpam-5300	41	17	e1	e1	NOUN
ejpam-5300	41	18	,	,	PUNCT
ejpam-5300	41	19	and	and	CCONJ
ejpam-5300	41	20	d1	d1	NOUN
ejpam-5300	41	21	respectively	respectively	ADV
ejpam-5300	41	22	,	,	PUNCT
ejpam-5300	41	23	and	and	CCONJ
ejpam-5300	41	24	circle	circle	NOUN
ejpam-5300	41	25	o2	o2	PROPN
ejpam-5300	41	26	is	be	AUX
ejpam-5300	41	27	tangent	tangent	NOUN
ejpam-5300	41	28	to	to	ADP
ejpam-5300	41	29	the	the	DET
ejpam-5300	41	30	sides	side	NOUN
ejpam-5300	41	31	ac1	ac1	PROPN
ejpam-5300	41	32	,	,	PUNCT
ejpam-5300	41	33	ab2	ab2	ADJ
ejpam-5300	41	34	,	,	PUNCT
ejpam-5300	41	35	and	and	CCONJ
ejpam-5300	42	1	b2c2	b2c2	ADP
ejpam-5300	42	2	at	at	ADP
ejpam-5300	42	3	points	point	NOUN
ejpam-5300	42	4	e2	e2	PROPN
ejpam-5300	42	5	,	,	PUNCT
ejpam-5300	42	6	f2	f2	PROPN
ejpam-5300	42	7	and	and	CCONJ
ejpam-5300	42	8	d2	d2	PROPN
ejpam-5300	42	9	respectively	respectively	ADV
ejpam-5300	42	10	by	by	ADP
ejpam-5300	42	11	specifying	specify	VERB
ejpam-5300	42	12	that	that	SCONJ
ejpam-5300	42	13	,	,	PUNCT
ejpam-5300	42	14	(	(	PUNCT
ejpam-5300	42	15	i	i	NOUN
ejpam-5300	42	16	)	)	PUNCT
ejpam-5300	42	17	|b1c1|	|b1c1|	PROPN
ejpam-5300	43	1	=	=	SYM
ejpam-5300	43	2	a	a	X
ejpam-5300	43	3	,	,	PUNCT
ejpam-5300	43	4	|ab1|	|ab1|	PROPN
ejpam-5300	43	5	=	=	SYM
ejpam-5300	43	6	c	c	NOUN
ejpam-5300	43	7	,	,	PUNCT
ejpam-5300	43	8	|c1a|	|c1a|	PROPN
ejpam-5300	43	9	=	=	SYM
ejpam-5300	43	10	b.	b.	PROPN
ejpam-5300	43	11	(	(	PUNCT
ejpam-5300	43	12	ii	ii	NOUN
ejpam-5300	43	13	)	)	PUNCT
ejpam-5300	43	14	|af1|	|af1|	NOUN
ejpam-5300	43	15	=	=	SYM
ejpam-5300	43	16	x2	x2	PROPN
ejpam-5300	43	17	,	,	PUNCT
ejpam-5300	43	18	|f1b1|	|f1b1|	X
ejpam-5300	43	19	=	=	SYM
ejpam-5300	43	20	x1	x1	PROPN
ejpam-5300	43	21	,	,	PUNCT
ejpam-5300	43	22	|ae2|	|ae2|	PROPN
ejpam-5300	43	23	=	=	SYM
ejpam-5300	43	24	y1	y1	PROPN
ejpam-5300	43	25	,	,	PUNCT
ejpam-5300	43	26	|d2b2|	|d2b2|	X
ejpam-5300	43	27	=	=	SYM
ejpam-5300	43	28	x3	x3	ADJ
ejpam-5300	43	29	,	,	PUNCT
ejpam-5300	43	30	|e2c1|	|e2c1|	ADJ
ejpam-5300	43	31	=	=	SYM
ejpam-5300	43	32	y2	y2	PROPN
ejpam-5300	43	33	(	(	PUNCT
ejpam-5300	43	34	iii	iii	NOUN
ejpam-5300	43	35	)	)	PUNCT
ejpam-5300	43	36	∠ab1c1	∠ab1c1	NOUN
ejpam-5300	43	37	=	=	SYM
ejpam-5300	43	38	b	b	NOUN
ejpam-5300	43	39	,	,	PUNCT
ejpam-5300	43	40	∠ac1b1	∠ac1b1	ADJ
ejpam-5300	43	41	=	=	PUNCT
ejpam-5300	44	1	c	c	NOUN
ejpam-5300	44	2	,	,	PUNCT
ejpam-5300	44	3	and	and	CCONJ
ejpam-5300	44	4	∠b1ac1	∠b1ac1	PROPN
ejpam-5300	44	5	=	=	SYM
ejpam-5300	44	6	a	a	DET
ejpam-5300	44	7	(	(	PUNCT
ejpam-5300	44	8	iv	iv	NOUN
ejpam-5300	44	9	)	)	PUNCT
ejpam-5300	44	10	semi	semi	NOUN
ejpam-5300	44	11	-	-	NOUN
ejpam-5300	44	12	perimeter	perimeter	NOUN
ejpam-5300	44	13	of	of	ADP
ejpam-5300	44	14	ab1b2	ab1b2	PROPN
ejpam-5300	44	15	triangle	triangle	NOUN
ejpam-5300	44	16	:	:	PUNCT
ejpam-5300	44	17	s1	s1	NOUN
ejpam-5300	44	18	=	=	PUNCT
ejpam-5300	44	19	x1	x1	PROPN
ejpam-5300	45	1	+	+	CCONJ
ejpam-5300	45	2	x3	x3	ADJ
ejpam-5300	45	3	+	+	CCONJ
ejpam-5300	45	4	y1	y1	ADJ
ejpam-5300	45	5	(	(	PUNCT
ejpam-5300	45	6	v	v	NOUN
ejpam-5300	45	7	)	)	PUNCT
ejpam-5300	45	8	semi	semi	NOUN
ejpam-5300	45	9	-	-	NOUN
ejpam-5300	45	10	perimeter	perimeter	NOUN
ejpam-5300	45	11	of	of	ADP
ejpam-5300	45	12	ac1b2	ac1b2	PROPN
ejpam-5300	45	13	triangle	triangle	NOUN
ejpam-5300	45	14	:	:	PUNCT
ejpam-5300	45	15	s2	s2	NOUN
ejpam-5300	45	16	=	=	PUNCT
ejpam-5300	45	17	x3	x3	PROPN
ejpam-5300	45	18	+	+	CCONJ
ejpam-5300	45	19	y1	y1	NOUN
ejpam-5300	45	20	+	+	X
ejpam-5300	45	21	y2	y2	PROPN
ejpam-5300	45	22	(	(	PUNCT
ejpam-5300	45	23	vi	vi	NOUN
ejpam-5300	45	24	)	)	PUNCT
ejpam-5300	45	25	semi	semi	NOUN
ejpam-5300	45	26	-	-	NOUN
ejpam-5300	45	27	perimeter	perimeter	NOUN
ejpam-5300	45	28	of	of	ADP
ejpam-5300	45	29	abc	abc	PROPN
ejpam-5300	45	30	triangle	triangle	VERB
ejpam-5300	45	31	:	:	PUNCT
ejpam-5300	45	32	s	s	X
ejpam-5300	45	33	=	=	NOUN
ejpam-5300	45	34	a+b+c	a+b+c	NOUN
ejpam-5300	45	35	2	2	NUM
ejpam-5300	45	36	=	=	SYM
ejpam-5300	45	37	x1	x1	PROPN
ejpam-5300	46	1	+	+	PUNCT
ejpam-5300	46	2	y3	y3	NOUN
ejpam-5300	46	3	+	+	CCONJ
ejpam-5300	46	4	y2	y2	PROPN
ejpam-5300	47	1	+	+	CCONJ
ejpam-5300	47	2	x3	x3	ADJ
ejpam-5300	47	3	and	and	CCONJ
ejpam-5300	47	4	then	then	ADV
ejpam-5300	47	5	,	,	PUNCT
ejpam-5300	47	6	r1	r1	PROPN
ejpam-5300	47	7	r2	r2	PROPN
ejpam-5300	47	8	=	=	PUNCT
ejpam-5300	48	1	tan	tan	PROPN
ejpam-5300	48	2	b	b	PROPN
ejpam-5300	48	3	2	2	NUM
ejpam-5300	48	4	·	·	PUNCT
ejpam-5300	48	5	(	(	PUNCT
ejpam-5300	48	6	s1	s1	PROPN
ejpam-5300	48	7	−	−	PROPN
ejpam-5300	48	8	(	(	PUNCT
ejpam-5300	48	9	x3	x3	PROPN
ejpam-5300	48	10	+	+	CCONJ
ejpam-5300	48	11	y1	y1	NOUN
ejpam-5300	48	12	)	)	PUNCT
ejpam-5300	48	13	)	)	PUNCT
ejpam-5300	49	1	tan	tan	PROPN
ejpam-5300	49	2	c	c	NOUN
ejpam-5300	49	3	2	2	NUM
ejpam-5300	49	4	·	·	PUNCT
ejpam-5300	49	5	(	(	PUNCT
ejpam-5300	49	6	s2	s2	NOUN
ejpam-5300	49	7	−	−	PROPN
ejpam-5300	50	1	(	(	PUNCT
ejpam-5300	50	2	x3	x3	PROPN
ejpam-5300	50	3	+	+	CCONJ
ejpam-5300	50	4	y1	y1	NOUN
ejpam-5300	50	5	)	)	PUNCT
ejpam-5300	50	6	)	)	PUNCT
ejpam-5300	50	7	figure	figure	NOUN
ejpam-5300	50	8	4	4	NUM
ejpam-5300	50	9	:	:	PUNCT
ejpam-5300	50	10	the	the	DET
ejpam-5300	50	11	image	image	NOUN
ejpam-5300	50	12	depicted	depict	VERB
ejpam-5300	50	13	the	the	DET
ejpam-5300	50	14	sangaku	sangaku	NOUN
ejpam-5300	50	15	two	two	NUM
ejpam-5300	50	16	circles	circle	NOUN
ejpam-5300	50	17	problem	problem	NOUN
ejpam-5300	50	18	.	.	PUNCT
ejpam-5300	51	1	proof	proof	NOUN
ejpam-5300	51	2	.	.	PUNCT
ejpam-5300	52	1	let	let	VERB
ejpam-5300	52	2	us	we	PRON
ejpam-5300	52	3	begin	begin	VERB
ejpam-5300	52	4	to	to	PART
ejpam-5300	52	5	consider	consider	VERB
ejpam-5300	52	6	the	the	DET
ejpam-5300	52	7	radius	radius	NOUN
ejpam-5300	52	8	of	of	ADP
ejpam-5300	52	9	two	two	NUM
ejpam-5300	52	10	incircles	incircle	NOUN
ejpam-5300	52	11	(	(	PUNCT
ejpam-5300	52	12	green	green	ADJ
ejpam-5300	52	13	and	and	CCONJ
ejpam-5300	52	14	blue	blue	ADJ
ejpam-5300	52	15	)	)	PUNCT
ejpam-5300	52	16	,	,	PUNCT
ejpam-5300	52	17	using	use	VERB
ejpam-5300	52	18	the	the	DET
ejpam-5300	52	19	incircle	incircle	NOUN
ejpam-5300	52	20	of	of	ADP
ejpam-5300	52	21	a	a	DET
ejpam-5300	52	22	triangle	triangle	NOUN
ejpam-5300	52	23	formulation	formulation	NOUN
ejpam-5300	52	24	.	.	PUNCT
ejpam-5300	53	1	we	we	PRON
ejpam-5300	53	2	get	get	VERB
ejpam-5300	53	3	,	,	PUNCT
ejpam-5300	53	4	r1	r1	NOUN
ejpam-5300	53	5	=	=	PUNCT
ejpam-5300	54	1	[	[	X
ejpam-5300	54	2	ab1b2	ab1b2	PROPN
ejpam-5300	54	3	]	]	X
ejpam-5300	54	4	s1	s1	NOUN
ejpam-5300	54	5	(	(	PUNCT
ejpam-5300	54	6	1	1	NUM
ejpam-5300	54	7	)	)	PUNCT
ejpam-5300	54	8	r2	r2	NOUN
ejpam-5300	54	9	=	=	PUNCT
ejpam-5300	55	1	[	[	X
ejpam-5300	55	2	ab2c1	ab2c1	X
ejpam-5300	55	3	]	]	X
ejpam-5300	55	4	s2	s2	NOUN
ejpam-5300	55	5	(	(	PUNCT
ejpam-5300	55	6	2	2	NUM
ejpam-5300	55	7	)	)	PUNCT
ejpam-5300	55	8	p.	p.	NOUN
ejpam-5300	55	9	boonsomchua	boonsomchua	PROPN
ejpam-5300	55	10	/	/	SYM
ejpam-5300	55	11	eur	eur	PROPN
ejpam-5300	55	12	.	.	PUNCT
ejpam-5300	56	1	j.	j.	PROPN
ejpam-5300	56	2	pure	pure	PROPN
ejpam-5300	56	3	appl	appl	PROPN
ejpam-5300	56	4	.	.	PROPN
ejpam-5300	56	5	math	math	PROPN
ejpam-5300	56	6	,	,	PUNCT
ejpam-5300	56	7	17	17	NUM
ejpam-5300	56	8	(	(	PUNCT
ejpam-5300	56	9	4	4	NUM
ejpam-5300	56	10	)	)	PUNCT
ejpam-5300	56	11	(	(	PUNCT
ejpam-5300	56	12	2024	2024	NUM
ejpam-5300	56	13	)	)	PUNCT
ejpam-5300	56	14	,	,	PUNCT
ejpam-5300	56	15	4135	4135	NUM
ejpam-5300	56	16	-	-	SYM
ejpam-5300	56	17	4146	4146	NUM
ejpam-5300	56	18	4138	4138	NUM
ejpam-5300	56	19	divided	divide	VERB
ejpam-5300	56	20	the	the	DET
ejpam-5300	56	21	equation	equation	NOUN
ejpam-5300	56	22	(	(	PUNCT
ejpam-5300	56	23	1	1	NUM
ejpam-5300	56	24	)	)	PUNCT
ejpam-5300	56	25	by	by	ADP
ejpam-5300	56	26	equation	equation	NOUN
ejpam-5300	56	27	(	(	PUNCT
ejpam-5300	56	28	2	2	NUM
ejpam-5300	56	29	)	)	PUNCT
ejpam-5300	56	30	.	.	PUNCT
ejpam-5300	57	1	then	then	ADV
ejpam-5300	57	2	,	,	PUNCT
ejpam-5300	57	3	r1	r1	NOUN
ejpam-5300	57	4	r2	r2	PROPN
ejpam-5300	57	5	=	=	PUNCT
ejpam-5300	58	1	[	[	X
ejpam-5300	58	2	ab1b2	ab1b2	X
ejpam-5300	58	3	]	]	X
ejpam-5300	58	4	[	[	X
ejpam-5300	58	5	ac1b2	ac1b2	X
ejpam-5300	58	6	]	]	PUNCT
ejpam-5300	58	7	·	·	PUNCT
ejpam-5300	58	8	s2	s2	NOUN
ejpam-5300	58	9	s1	s1	NOUN
ejpam-5300	58	10	(	(	PUNCT
ejpam-5300	58	11	3	3	NUM
ejpam-5300	58	12	)	)	PUNCT
ejpam-5300	58	13	from	from	ADP
ejpam-5300	58	14	the	the	DET
ejpam-5300	58	15	area	area	NOUN
ejpam-5300	58	16	-	-	PUNCT
ejpam-5300	58	17	based	base	VERB
ejpam-5300	58	18	ratio	ratio	NOUN
ejpam-5300	58	19	,	,	PUNCT
ejpam-5300	58	20	we	we	PRON
ejpam-5300	58	21	can	can	AUX
ejpam-5300	58	22	formulate	formulate	VERB
ejpam-5300	58	23	the	the	DET
ejpam-5300	58	24	area	area	NOUN
ejpam-5300	58	25	proportion	proportion	NOUN
ejpam-5300	58	26	of	of	ADP
ejpam-5300	58	27	two	two	NUM
ejpam-5300	58	28	sub	sub	ADJ
ejpam-5300	58	29	-	-	ADJ
ejpam-5300	58	30	triangles	triangles	ADJ
ejpam-5300	58	31	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	58	32	and	and	CCONJ
ejpam-5300	58	33	∆ac1b2	∆ac1b2	VERB
ejpam-5300	58	34	depending	depend	VERB
ejpam-5300	58	35	on	on	ADP
ejpam-5300	58	36	its	its	PRON
ejpam-5300	58	37	bases	basis	NOUN
ejpam-5300	58	38	.	.	PUNCT
ejpam-5300	59	1	[	[	X
ejpam-5300	59	2	ab1b2	ab1b2	X
ejpam-5300	59	3	]	]	X
ejpam-5300	59	4	[	[	X
ejpam-5300	59	5	ac1b2	ac1b2	X
ejpam-5300	59	6	]	]	X
ejpam-5300	59	7	=	=	SYM
ejpam-5300	59	8	(	(	PUNCT
ejpam-5300	59	9	s1	s1	PROPN
ejpam-5300	59	10	−	−	PROPN
ejpam-5300	59	11	x2	x2	PROPN
ejpam-5300	59	12	)	)	PUNCT
ejpam-5300	59	13	(	(	PUNCT
ejpam-5300	59	14	s2	s2	NOUN
ejpam-5300	59	15	−	−	PROPN
ejpam-5300	59	16	y1	y1	PROPN
ejpam-5300	59	17	)	)	PUNCT
ejpam-5300	59	18	(	(	PUNCT
ejpam-5300	59	19	4	4	X
ejpam-5300	59	20	)	)	PUNCT
ejpam-5300	59	21	substituting	substitute	VERB
ejpam-5300	59	22	equation	equation	NOUN
ejpam-5300	59	23	(	(	PUNCT
ejpam-5300	59	24	3	3	NUM
ejpam-5300	59	25	)	)	PUNCT
ejpam-5300	59	26	into	into	ADP
ejpam-5300	59	27	equation	equation	NOUN
ejpam-5300	59	28	(	(	PUNCT
ejpam-5300	59	29	4	4	NUM
ejpam-5300	59	30	)	)	PUNCT
ejpam-5300	59	31	and	and	CCONJ
ejpam-5300	59	32	we	we	PRON
ejpam-5300	59	33	arrive	arrive	VERB
ejpam-5300	59	34	at	at	ADP
ejpam-5300	59	35	r1	r1	PROPN
ejpam-5300	59	36	r2	r2	PROPN
ejpam-5300	59	37	=	=	SYM
ejpam-5300	59	38	s2	s2	PROPN
ejpam-5300	59	39	s1	s1	NOUN
ejpam-5300	59	40	·	·	PUNCT
ejpam-5300	59	41	(	(	PUNCT
ejpam-5300	59	42	s1	s1	PROPN
ejpam-5300	59	43	−	−	PROPN
ejpam-5300	59	44	x2	x2	PROPN
ejpam-5300	59	45	)	)	PUNCT
ejpam-5300	59	46	(	(	PUNCT
ejpam-5300	59	47	s2	s2	NOUN
ejpam-5300	59	48	−	−	PROPN
ejpam-5300	59	49	y1	y1	PROPN
ejpam-5300	59	50	)	)	PUNCT
ejpam-5300	59	51	(	(	PUNCT
ejpam-5300	59	52	5	5	X
ejpam-5300	59	53	)	)	PUNCT
ejpam-5300	59	54	this	this	DET
ejpam-5300	59	55	equation	equation	NOUN
ejpam-5300	59	56	is	be	AUX
ejpam-5300	59	57	straightforward	straightforward	ADJ
ejpam-5300	59	58	;	;	PUNCT
ejpam-5300	59	59	to	to	PART
ejpam-5300	59	60	derive	derive	VERB
ejpam-5300	59	61	in	in	ADP
ejpam-5300	59	62	terms	term	NOUN
ejpam-5300	59	63	of	of	ADP
ejpam-5300	59	64	bisector	bisector	NOUN
ejpam-5300	59	65	-	-	PUNCT
ejpam-5300	59	66	angle	angle	NOUN
ejpam-5300	59	67	trigonometry	trigonometry	NOUN
ejpam-5300	59	68	.	.	PUNCT
ejpam-5300	60	1	tan	tan	PROPN
ejpam-5300	60	2	(	(	PUNCT
ejpam-5300	60	3	b	b	PROPN
ejpam-5300	60	4	2	2	NUM
ejpam-5300	60	5	)	)	PUNCT
ejpam-5300	60	6	=	=	SYM
ejpam-5300	60	7	r1	r1	NOUN
ejpam-5300	60	8	s1	s1	PROPN
ejpam-5300	60	9	−	−	PROPN
ejpam-5300	61	1	(	(	PUNCT
ejpam-5300	61	2	y1	y1	INTJ
ejpam-5300	61	3	+	+	CCONJ
ejpam-5300	61	4	x3	x3	ADJ
ejpam-5300	61	5	)	)	PUNCT
ejpam-5300	61	6	,	,	PUNCT
ejpam-5300	61	7	tan	tan	PROPN
ejpam-5300	61	8	(	(	PUNCT
ejpam-5300	61	9	c	c	NOUN
ejpam-5300	61	10	2	2	NUM
ejpam-5300	61	11	)	)	PUNCT
ejpam-5300	61	12	=	=	SYM
ejpam-5300	61	13	r2	r2	PROPN
ejpam-5300	61	14	s2	s2	NOUN
ejpam-5300	61	15	−	−	PROPN
ejpam-5300	62	1	(	(	PUNCT
ejpam-5300	62	2	y1	y1	INTJ
ejpam-5300	62	3	+	+	CCONJ
ejpam-5300	62	4	x3	x3	ADJ
ejpam-5300	62	5	)	)	PUNCT
ejpam-5300	62	6	hence	hence	ADV
ejpam-5300	62	7	,	,	PUNCT
ejpam-5300	62	8	tan	tan	PROPN
ejpam-5300	62	9	b	b	PROPN
ejpam-5300	62	10	2	2	NUM
ejpam-5300	62	11	tan	tan	NOUN
ejpam-5300	62	12	c	c	NOUN
ejpam-5300	62	13	2	2	NUM
ejpam-5300	62	14	=	=	SYM
ejpam-5300	62	15	r1	r1	NOUN
ejpam-5300	62	16	r2	r2	PROPN
ejpam-5300	62	17	·	·	PUNCT
ejpam-5300	62	18	(	(	PUNCT
ejpam-5300	62	19	s2	s2	NOUN
ejpam-5300	62	20	−	−	PROPN
ejpam-5300	62	21	(	(	PUNCT
ejpam-5300	62	22	y1	y1	INTJ
ejpam-5300	62	23	+	+	CCONJ
ejpam-5300	62	24	x3	x3	ADJ
ejpam-5300	62	25	)	)	PUNCT
ejpam-5300	62	26	)	)	PUNCT
ejpam-5300	62	27	(	(	PUNCT
ejpam-5300	62	28	s1	s1	PROPN
ejpam-5300	62	29	−	−	PROPN
ejpam-5300	62	30	(	(	PUNCT
ejpam-5300	62	31	y1	y1	INTJ
ejpam-5300	62	32	+	+	CCONJ
ejpam-5300	62	33	x3	x3	ADJ
ejpam-5300	62	34	)	)	PUNCT
ejpam-5300	62	35	)	)	PUNCT
ejpam-5300	62	36	⇔	⇔	PROPN
ejpam-5300	62	37	r1	r1	PROPN
ejpam-5300	62	38	r2	r2	PROPN
ejpam-5300	62	39	=	=	PUNCT
ejpam-5300	62	40	tan	tan	PROPN
ejpam-5300	62	41	b	b	PROPN
ejpam-5300	62	42	2	2	NUM
ejpam-5300	62	43	·	·	PUNCT
ejpam-5300	62	44	(	(	PUNCT
ejpam-5300	62	45	s1	s1	PROPN
ejpam-5300	62	46	−	−	PROPN
ejpam-5300	62	47	(	(	PUNCT
ejpam-5300	62	48	x3	x3	PROPN
ejpam-5300	62	49	+	+	CCONJ
ejpam-5300	62	50	y1	y1	NOUN
ejpam-5300	62	51	)	)	PUNCT
ejpam-5300	62	52	)	)	PUNCT
ejpam-5300	62	53	tan	tan	PROPN
ejpam-5300	62	54	c	c	NOUN
ejpam-5300	62	55	2	2	NUM
ejpam-5300	62	56	·	·	PUNCT
ejpam-5300	62	57	(	(	PUNCT
ejpam-5300	62	58	s2	s2	NOUN
ejpam-5300	62	59	−	−	PROPN
ejpam-5300	63	1	(	(	PUNCT
ejpam-5300	63	2	x3	x3	PROPN
ejpam-5300	63	3	+	+	CCONJ
ejpam-5300	63	4	y1	y1	NOUN
ejpam-5300	63	5	)	)	PUNCT
ejpam-5300	63	6	)	)	PUNCT
ejpam-5300	64	1	suppose	suppose	VERB
ejpam-5300	64	2	the	the	DET
ejpam-5300	64	3	biggest	big	ADJ
ejpam-5300	64	4	right	right	ADJ
ejpam-5300	64	5	triangle	triangle	NOUN
ejpam-5300	64	6	,	,	PUNCT
ejpam-5300	64	7	∆ac1b1	∆ac1b1	NOUN
ejpam-5300	64	8	,	,	PUNCT
ejpam-5300	64	9	obtained	obtain	VERB
ejpam-5300	64	10	a	a	DET
ejpam-5300	64	11	perpendicular	perpendicular	ADJ
ejpam-5300	64	12	line	line	NOUN
ejpam-5300	64	13	from	from	ADP
ejpam-5300	64	14	vertex	vertex	NOUN
ejpam-5300	64	15	a.	a.	NOUN
ejpam-5300	64	16	in	in	ADP
ejpam-5300	64	17	that	that	DET
ejpam-5300	64	18	case	case	NOUN
ejpam-5300	64	19	,	,	PUNCT
ejpam-5300	64	20	this	this	DET
ejpam-5300	64	21	scenario	scenario	NOUN
ejpam-5300	64	22	can	can	AUX
ejpam-5300	64	23	extend	extend	VERB
ejpam-5300	64	24	to	to	ADP
ejpam-5300	64	25	the	the	DET
ejpam-5300	64	26	scope	scope	NOUN
ejpam-5300	64	27	of	of	ADP
ejpam-5300	64	28	mathematical	mathematical	ADJ
ejpam-5300	64	29	formulation	formulation	NOUN
ejpam-5300	64	30	that	that	PRON
ejpam-5300	64	31	describes	describe	VERB
ejpam-5300	64	32	two	two	NUM
ejpam-5300	64	33	tangent	tangent	ADJ
ejpam-5300	64	34	circles	circle	NOUN
ejpam-5300	64	35	in	in	ADP
ejpam-5300	64	36	a	a	DET
ejpam-5300	64	37	triangle	triangle	NOUN
ejpam-5300	64	38	with	with	ADP
ejpam-5300	64	39	a	a	DET
ejpam-5300	64	40	perpendicular	perpendicular	ADJ
ejpam-5300	64	41	line	line	NOUN
ejpam-5300	64	42	.	.	PUNCT
ejpam-5300	65	1	corollary	corollary	ADJ
ejpam-5300	65	2	1	1	NUM
ejpam-5300	65	3	(	(	PUNCT
ejpam-5300	65	4	perpendicular	perpendicular	ADJ
ejpam-5300	65	5	triangle	triangle	NOUN
ejpam-5300	65	6	scenario	scenario	NOUN
ejpam-5300	65	7	)	)	PUNCT
ejpam-5300	65	8	consider	consider	VERB
ejpam-5300	65	9	a	a	DET
ejpam-5300	65	10	triangle	triangle	NOUN
ejpam-5300	65	11	△	△	X
ejpam-5300	65	12	ab1c1	ab1c1	X
ejpam-5300	65	13	with	with	ADP
ejpam-5300	65	14	vertices	vertex	NOUN
ejpam-5300	65	15	a	a	PRON
ejpam-5300	65	16	,	,	PUNCT
ejpam-5300	65	17	b1	b1	NOUN
ejpam-5300	65	18	,	,	PUNCT
ejpam-5300	65	19	and	and	CCONJ
ejpam-5300	65	20	c1	c1	PROPN
ejpam-5300	65	21	.	.	PUNCT
ejpam-5300	66	1	inside	inside	ADP
ejpam-5300	66	2	this	this	DET
ejpam-5300	66	3	triangle	triangle	NOUN
ejpam-5300	66	4	,	,	PUNCT
ejpam-5300	66	5	there	there	PRON
ejpam-5300	66	6	are	be	VERB
ejpam-5300	66	7	three	three	NUM
ejpam-5300	66	8	inscribed	inscribe	VERB
ejpam-5300	66	9	circles	circle	NOUN
ejpam-5300	66	10	.	.	PUNCT
ejpam-5300	67	1	let	let	VERB
ejpam-5300	67	2	o1	o1	NOUN
ejpam-5300	67	3	(	(	PUNCT
ejpam-5300	67	4	green	green	ADJ
ejpam-5300	67	5	)	)	PUNCT
ejpam-5300	67	6	,	,	PUNCT
ejpam-5300	67	7	o2	o2	PROPN
ejpam-5300	67	8	(	(	PUNCT
ejpam-5300	67	9	blue	blue	ADJ
ejpam-5300	67	10	)	)	PUNCT
ejpam-5300	67	11	,	,	PUNCT
ejpam-5300	67	12	and	and	CCONJ
ejpam-5300	67	13	o3	o3	PROPN
ejpam-5300	67	14	(	(	PUNCT
ejpam-5300	67	15	light	light	ADJ
ejpam-5300	67	16	gray	gray	NOUN
ejpam-5300	67	17	)	)	PUNCT
ejpam-5300	67	18	be	be	VERB
ejpam-5300	67	19	the	the	DET
ejpam-5300	67	20	incircles	incircle	NOUN
ejpam-5300	67	21	of	of	ADP
ejpam-5300	67	22	triangles	triangle	NOUN
ejpam-5300	67	23	△	△	PROPN
ejpam-5300	67	24	ab1b2	ab1b2	PROPN
ejpam-5300	67	25	,	,	PUNCT
ejpam-5300	67	26	△	△	PROPN
ejpam-5300	67	27	ac1b2	ac1b2	PROPN
ejpam-5300	67	28	,	,	PUNCT
ejpam-5300	67	29	and	and	CCONJ
ejpam-5300	68	1	△	△	PUNCT
ejpam-5300	68	2	ab1c1	ab1c1	X
ejpam-5300	68	3	with	with	ADP
ejpam-5300	68	4	radii	radius	NOUN
ejpam-5300	68	5	r1	r1	NOUN
ejpam-5300	68	6	,	,	PUNCT
ejpam-5300	68	7	r2	r2	NOUN
ejpam-5300	68	8	,	,	PUNCT
ejpam-5300	68	9	and	and	CCONJ
ejpam-5300	68	10	r	r	NOUN
ejpam-5300	68	11	respectively	respectively	ADV
ejpam-5300	68	12	.	.	PUNCT
ejpam-5300	69	1	circle	circle	PROPN
ejpam-5300	69	2	o1	o1	PROPN
ejpam-5300	69	3	is	be	AUX
ejpam-5300	69	4	tangent	tangent	NOUN
ejpam-5300	69	5	to	to	ADP
ejpam-5300	69	6	sides	side	NOUN
ejpam-5300	69	7	ab1	ab1	ADV
ejpam-5300	69	8	,	,	PUNCT
ejpam-5300	69	9	ab2	ab2	NOUN
ejpam-5300	69	10	and	and	CCONJ
ejpam-5300	69	11	b1b2	b1b2	VERB
ejpam-5300	69	12	at	at	ADP
ejpam-5300	69	13	points	point	NOUN
ejpam-5300	69	14	f1	f1	NOUN
ejpam-5300	69	15	and	and	CCONJ
ejpam-5300	69	16	e1	e1	NOUN
ejpam-5300	69	17	,	,	PUNCT
ejpam-5300	69	18	and	and	CCONJ
ejpam-5300	69	19	d1	d1	NOUN
ejpam-5300	69	20	respectively	respectively	ADV
ejpam-5300	69	21	,	,	PUNCT
ejpam-5300	69	22	and	and	CCONJ
ejpam-5300	69	23	circle	circle	NOUN
ejpam-5300	69	24	o2	o2	PROPN
ejpam-5300	69	25	is	be	AUX
ejpam-5300	69	26	tangent	tangent	NOUN
ejpam-5300	69	27	to	to	ADP
ejpam-5300	69	28	sides	side	NOUN
ejpam-5300	69	29	ac1	ac1	PROPN
ejpam-5300	69	30	,	,	PUNCT
ejpam-5300	69	31	ab2	ab2	NOUN
ejpam-5300	69	32	and	and	CCONJ
ejpam-5300	69	33	c1b2	c1b2	NOUN
ejpam-5300	69	34	at	at	ADP
ejpam-5300	69	35	points	point	NOUN
ejpam-5300	69	36	e2	e2	PROPN
ejpam-5300	69	37	,	,	PUNCT
ejpam-5300	69	38	f2	f2	PROPN
ejpam-5300	69	39	and	and	CCONJ
ejpam-5300	69	40	d2	d2	PROPN
ejpam-5300	69	41	respectively	respectively	ADV
ejpam-5300	69	42	.	.	PUNCT
ejpam-5300	70	1	circle	circle	PROPN
ejpam-5300	70	2	o3	o3	PROPN
ejpam-5300	70	3	is	be	AUX
ejpam-5300	70	4	tangent	tangent	NOUN
ejpam-5300	70	5	to	to	ADP
ejpam-5300	70	6	sides	side	NOUN
ejpam-5300	70	7	ab1	ab1	ADV
ejpam-5300	70	8	,	,	PUNCT
ejpam-5300	70	9	ac1	ac1	PROPN
ejpam-5300	70	10	,	,	PUNCT
ejpam-5300	70	11	and	and	CCONJ
ejpam-5300	70	12	b1c1	b1c1	VERB
ejpam-5300	70	13	at	at	ADP
ejpam-5300	70	14	points	point	NOUN
ejpam-5300	70	15	t1	t1	PROPN
ejpam-5300	70	16	,	,	PUNCT
ejpam-5300	70	17	t2	t2	NOUN
ejpam-5300	70	18	,	,	PUNCT
ejpam-5300	70	19	and	and	CCONJ
ejpam-5300	70	20	t3	t3	NOUN
ejpam-5300	70	21	,	,	PUNCT
ejpam-5300	70	22	respectively	respectively	ADV
ejpam-5300	70	23	such	such	ADJ
ejpam-5300	70	24	that	that	SCONJ
ejpam-5300	70	25	the	the	DET
ejpam-5300	70	26	following	follow	VERB
ejpam-5300	70	27	conditions	condition	NOUN
ejpam-5300	70	28	hold	hold	VERB
ejpam-5300	70	29	:	:	PUNCT
ejpam-5300	70	30	(	(	PUNCT
ejpam-5300	70	31	i	i	NOUN
ejpam-5300	70	32	)	)	PUNCT
ejpam-5300	70	33	b1a	b1a	PROPN
ejpam-5300	70	34	⊥	⊥	PROPN
ejpam-5300	70	35	c1a	c1a	PROPN
ejpam-5300	70	36	.	.	PUNCT
ejpam-5300	71	1	(	(	PUNCT
ejpam-5300	71	2	ii	ii	NOUN
ejpam-5300	71	3	)	)	PUNCT
ejpam-5300	71	4	ab2	ab2	NOUN
ejpam-5300	71	5	⊥	⊥	PROPN
ejpam-5300	71	6	b1c1	b1c1	PROPN
ejpam-5300	71	7	.	.	PUNCT
ejpam-5300	72	1	and	and	CCONJ
ejpam-5300	72	2	then	then	ADV
ejpam-5300	72	3	,	,	PUNCT
ejpam-5300	72	4	ab2	ab2	NOUN
ejpam-5300	72	5	=	=	SYM
ejpam-5300	72	6	√	√	PROPN
ejpam-5300	72	7	(	(	PUNCT
ejpam-5300	72	8	s1	s1	PROPN
ejpam-5300	72	9	−	−	PROPN
ejpam-5300	72	10	x2)(s2	x2)(s2	PUNCT
ejpam-5300	73	1	−	−	PROPN
ejpam-5300	73	2	y1	y1	NOUN
ejpam-5300	73	3	)	)	PUNCT
ejpam-5300	73	4	proof	proof	NOUN
ejpam-5300	73	5	.	.	PUNCT
ejpam-5300	74	1	we	we	PRON
ejpam-5300	74	2	know	know	VERB
ejpam-5300	74	3	that	that	SCONJ
ejpam-5300	74	4	the	the	DET
ejpam-5300	74	5	incenter	incenter	NOUN
ejpam-5300	74	6	of	of	ADP
ejpam-5300	74	7	circle	circle	NOUN
ejpam-5300	74	8	o	o	PROPN
ejpam-5300	74	9	lies	lie	VERB
ejpam-5300	74	10	on	on	ADP
ejpam-5300	74	11	the	the	DET
ejpam-5300	74	12	line	line	NOUN
ejpam-5300	74	13	ab2	ab2	ADJ
ejpam-5300	74	14	,	,	PUNCT
ejpam-5300	74	15	with	with	ADP
ejpam-5300	74	16	points	point	NOUN
ejpam-5300	74	17	b2	b2	NOUN
ejpam-5300	74	18	and	and	CCONJ
ejpam-5300	74	19	t1	t1	NOUN
ejpam-5300	74	20	coinciding	coincide	VERB
ejpam-5300	74	21	in	in	ADP
ejpam-5300	74	22	this	this	DET
ejpam-5300	74	23	case	case	NOUN
ejpam-5300	74	24	.	.	PUNCT
ejpam-5300	75	1	therefore	therefore	ADV
ejpam-5300	75	2	,	,	PUNCT
ejpam-5300	75	3	at1it2	at1it2	NOUN
ejpam-5300	75	4	forms	form	VERB
ejpam-5300	75	5	a	a	DET
ejpam-5300	75	6	square	square	NOUN
ejpam-5300	75	7	,	,	PUNCT
ejpam-5300	75	8	as	as	SCONJ
ejpam-5300	75	9	all	all	PRON
ejpam-5300	75	10	its	its	PRON
ejpam-5300	75	11	sides	side	NOUN
ejpam-5300	75	12	are	be	AUX
ejpam-5300	75	13	equal	equal	ADJ
ejpam-5300	75	14	to	to	ADP
ejpam-5300	75	15	the	the	DET
ejpam-5300	75	16	radius	radius	NOUN
ejpam-5300	75	17	of	of	ADP
ejpam-5300	75	18	the	the	DET
ejpam-5300	75	19	circle	circle	NOUN
ejpam-5300	76	1	o.	o.	NOUN
ejpam-5300	76	2	it	it	PRON
ejpam-5300	76	3	follows	follow	VERB
ejpam-5300	76	4	that	that	PRON
ejpam-5300	76	5	b+	b+	ADP
ejpam-5300	76	6	c	c	X
ejpam-5300	76	7	=	=	SYM
ejpam-5300	76	8	2r	2r	NUM
ejpam-5300	76	9	+	+	CCONJ
ejpam-5300	76	10	a	a	DET
ejpam-5300	76	11	consider	consider	VERB
ejpam-5300	76	12	the	the	DET
ejpam-5300	76	13	incircles	incircle	NOUN
ejpam-5300	76	14	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	76	15	and	and	CCONJ
ejpam-5300	76	16	∆ac1b2	∆ac1b2	NOUN
ejpam-5300	76	17	can	can	AUX
ejpam-5300	76	18	express	express	VERB
ejpam-5300	76	19	the	the	DET
ejpam-5300	76	20	connection	connection	NOUN
ejpam-5300	76	21	between	between	ADP
ejpam-5300	76	22	incircles	incircle	NOUN
ejpam-5300	76	23	radius	radius	NOUN
ejpam-5300	76	24	and	and	CCONJ
ejpam-5300	76	25	side	side	NOUN
ejpam-5300	76	26	ab1	ab1	ADV
ejpam-5300	76	27	,	,	PUNCT
ejpam-5300	76	28	influencing	influence	VERB
ejpam-5300	76	29	useful	useful	ADJ
ejpam-5300	76	30	mathematical	mathematical	ADJ
ejpam-5300	76	31	formulation	formulation	NOUN
ejpam-5300	76	32	after	after	ADP
ejpam-5300	76	33	combined	combine	VERB
ejpam-5300	76	34	for	for	ADP
ejpam-5300	76	35	each	each	DET
ejpam-5300	76	36	other	other	ADJ
ejpam-5300	76	37	.	.	PUNCT
ejpam-5300	77	1	p.	p.	NOUN
ejpam-5300	77	2	boonsomchua	boonsomchua	PROPN
ejpam-5300	77	3	/	/	SYM
ejpam-5300	77	4	eur	eur	PROPN
ejpam-5300	77	5	.	.	PUNCT
ejpam-5300	78	1	j.	j.	PROPN
ejpam-5300	78	2	pure	pure	PROPN
ejpam-5300	78	3	appl	appl	PROPN
ejpam-5300	78	4	.	.	PROPN
ejpam-5300	78	5	math	math	PROPN
ejpam-5300	78	6	,	,	PUNCT
ejpam-5300	78	7	17	17	NUM
ejpam-5300	78	8	(	(	PUNCT
ejpam-5300	78	9	4	4	NUM
ejpam-5300	78	10	)	)	PUNCT
ejpam-5300	78	11	(	(	PUNCT
ejpam-5300	78	12	2024	2024	NUM
ejpam-5300	78	13	)	)	PUNCT
ejpam-5300	78	14	,	,	PUNCT
ejpam-5300	78	15	4135	4135	NUM
ejpam-5300	78	16	-	-	SYM
ejpam-5300	78	17	4146	4146	NUM
ejpam-5300	78	18	4139	4139	NUM
ejpam-5300	78	19	figure	figure	NOUN
ejpam-5300	78	20	5	5	NUM
ejpam-5300	78	21	:	:	PUNCT
ejpam-5300	78	22	the	the	DET
ejpam-5300	78	23	image	image	NOUN
ejpam-5300	78	24	depicts	depict	VERB
ejpam-5300	78	25	the	the	DET
ejpam-5300	78	26	sangaku	sangaku	NOUN
ejpam-5300	78	27	two	two	NUM
ejpam-5300	78	28	circles	circle	NOUN
ejpam-5300	78	29	problem	problem	NOUN
ejpam-5300	78	30	,	,	PUNCT
ejpam-5300	78	31	illustrating	illustrate	VERB
ejpam-5300	78	32	the	the	DET
ejpam-5300	78	33	perpendicular	perpendicular	ADJ
ejpam-5300	78	34	line	line	NOUN
ejpam-5300	78	35	ab2	ab2	PROPN
ejpam-5300	78	36	.	.	PUNCT
ejpam-5300	79	1	figure	figure	VERB
ejpam-5300	79	2	6	6	NUM
ejpam-5300	79	3	:	:	PUNCT
ejpam-5300	79	4	the	the	DET
ejpam-5300	79	5	image	image	NOUN
ejpam-5300	79	6	depicts	depict	VERB
ejpam-5300	79	7	the	the	DET
ejpam-5300	79	8	sangaku	sangaku	NOUN
ejpam-5300	79	9	two	two	NUM
ejpam-5300	79	10	circles	circle	NOUN
ejpam-5300	79	11	problem	problem	NOUN
ejpam-5300	79	12	featuring	feature	VERB
ejpam-5300	79	13	the	the	DET
ejpam-5300	79	14	inscribed	inscribe	VERB
ejpam-5300	79	15	circles	circle	NOUN
ejpam-5300	80	1	o.	o.	NOUN
ejpam-5300	80	2	2(r1	2(r1	PROPN
ejpam-5300	81	1	+	+	CCONJ
ejpam-5300	81	2	r2	r2	NOUN
ejpam-5300	81	3	)	)	PUNCT
ejpam-5300	82	1	+	+	NOUN
ejpam-5300	82	2	ab1	ab1	X
ejpam-5300	82	3	+	+	ADJ
ejpam-5300	82	4	ac1	ac1	NOUN
ejpam-5300	82	5	=	=	SYM
ejpam-5300	82	6	b1b2	b1b2	PROPN
ejpam-5300	82	7	+	+	ADJ
ejpam-5300	82	8	ab2	ab2	NOUN
ejpam-5300	82	9	+	+	X
ejpam-5300	82	10	c1b2	c1b2	X
ejpam-5300	82	11	+	+	ADJ
ejpam-5300	82	12	ab2	ab2	ADJ
ejpam-5300	82	13	further	far	ADV
ejpam-5300	82	14	simplifying	simplifying	NOUN
ejpam-5300	82	15	,	,	PUNCT
ejpam-5300	82	16	we	we	PRON
ejpam-5300	82	17	get	get	VERB
ejpam-5300	82	18	:	:	PUNCT
ejpam-5300	82	19	ab1	ab1	X
ejpam-5300	82	20	=	=	SYM
ejpam-5300	82	21	r1	r1	PROPN
ejpam-5300	82	22	+	+	NUM
ejpam-5300	82	23	r2	r2	PROPN
ejpam-5300	82	24	+	+	CCONJ
ejpam-5300	82	25	r	r	NOUN
ejpam-5300	82	26	(	(	PUNCT
ejpam-5300	82	27	6	6	NUM
ejpam-5300	82	28	)	)	PUNCT
ejpam-5300	82	29	we	we	PRON
ejpam-5300	82	30	derived	derive	VERB
ejpam-5300	82	31	the	the	DET
ejpam-5300	82	32	right	right	ADJ
ejpam-5300	82	33	-	-	PUNCT
ejpam-5300	82	34	hand	hand	NOUN
ejpam-5300	82	35	side	side	NOUN
ejpam-5300	82	36	of	of	ADP
ejpam-5300	82	37	the	the	DET
ejpam-5300	82	38	main	main	ADJ
ejpam-5300	82	39	formulation	formulation	NOUN
ejpam-5300	82	40	but	but	CCONJ
ejpam-5300	82	41	needed	need	VERB
ejpam-5300	82	42	to	to	PART
ejpam-5300	82	43	show	show	VERB
ejpam-5300	82	44	that	that	SCONJ
ejpam-5300	82	45	the	the	DET
ejpam-5300	82	46	left	left	ADJ
ejpam-5300	82	47	-	-	PUNCT
ejpam-5300	82	48	hand	hand	NOUN
ejpam-5300	82	49	side	side	NOUN
ejpam-5300	82	50	of	of	ADP
ejpam-5300	82	51	the	the	DET
ejpam-5300	82	52	equation	equation	NOUN
ejpam-5300	82	53	is	be	AUX
ejpam-5300	82	54	equal	equal	ADJ
ejpam-5300	82	55	to	to	ADP
ejpam-5300	82	56	the	the	DET
ejpam-5300	82	57	right	right	ADJ
ejpam-5300	82	58	-	-	PUNCT
ejpam-5300	82	59	hand	hand	NOUN
ejpam-5300	82	60	side	side	NOUN
ejpam-5300	82	61	,	,	PUNCT
ejpam-5300	82	62	demonstrating	demonstrate	VERB
ejpam-5300	82	63	the	the	DET
ejpam-5300	82	64	equality	equality	NOUN
ejpam-5300	82	65	between	between	ADP
ejpam-5300	82	66	both	both	DET
ejpam-5300	82	67	expressions	expression	NOUN
ejpam-5300	82	68	.	.	PUNCT
ejpam-5300	83	1	according	accord	VERB
ejpam-5300	83	2	to	to	ADP
ejpam-5300	83	3	the	the	DET
ejpam-5300	83	4	similar	similar	ADJ
ejpam-5300	83	5	triangle	triangle	NOUN
ejpam-5300	83	6	theorem	theorem	VERB
ejpam-5300	83	7	,	,	PUNCT
ejpam-5300	83	8	and	and	CCONJ
ejpam-5300	83	9	consider	consider	VERB
ejpam-5300	83	10	the	the	DET
ejpam-5300	83	11	triangle	triangle	NOUN
ejpam-5300	83	12	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	83	13	∼	∼	NOUN
ejpam-5300	83	14	∆ab2c1	∆ab2c1	NOUN
ejpam-5300	83	15	,	,	PUNCT
ejpam-5300	83	16	which	which	PRON
ejpam-5300	83	17	implies	imply	VERB
ejpam-5300	83	18	the	the	DET
ejpam-5300	83	19	following	following	NOUN
ejpam-5300	83	20	.	.	PUNCT
ejpam-5300	84	1	b1b2	b1b2	NOUN
ejpam-5300	84	2	ab1	ab1	ADV
ejpam-5300	85	1	=	=	PUNCT
ejpam-5300	85	2	ab1	ab1	X
ejpam-5300	85	3	b2c1	b2c1	X
ejpam-5300	85	4	=	=	VERB
ejpam-5300	85	5	⇒	⇒	VERB
ejpam-5300	85	6	ab2	ab2	NOUN
ejpam-5300	85	7	1	1	NUM
ejpam-5300	85	8	=	=	SYM
ejpam-5300	85	9	b1b2	b1b2	PROPN
ejpam-5300	85	10	·	·	PUNCT
ejpam-5300	85	11	b2c1	b2c1	X
ejpam-5300	85	12	(	(	PUNCT
ejpam-5300	85	13	7	7	X
ejpam-5300	85	14	)	)	PUNCT
ejpam-5300	85	15	substituting	substitute	VERB
ejpam-5300	85	16	equation	equation	NOUN
ejpam-5300	85	17	(	(	PUNCT
ejpam-5300	85	18	6	6	NUM
ejpam-5300	85	19	)	)	PUNCT
ejpam-5300	85	20	into	into	ADP
ejpam-5300	85	21	equation	equation	NOUN
ejpam-5300	85	22	(	(	PUNCT
ejpam-5300	85	23	7	7	NUM
ejpam-5300	85	24	)	)	PUNCT
ejpam-5300	85	25	and	and	CCONJ
ejpam-5300	85	26	we	we	PRON
ejpam-5300	85	27	arrive	arrive	VERB
ejpam-5300	85	28	at	at	ADP
ejpam-5300	85	29	ab2	ab2	NOUN
ejpam-5300	85	30	2	2	NUM
ejpam-5300	85	31	=	=	SYM
ejpam-5300	85	32	(	(	PUNCT
ejpam-5300	85	33	b1b2	b1b2	PROPN
ejpam-5300	85	34	)	)	PUNCT
ejpam-5300	85	35	·	·	PUNCT
ejpam-5300	85	36	(	(	PUNCT
ejpam-5300	85	37	c1b2	c1b2	NOUN
ejpam-5300	85	38	)	)	PUNCT
ejpam-5300	85	39	=	=	SYM
ejpam-5300	86	1	(	(	PUNCT
ejpam-5300	86	2	x1	x1	PROPN
ejpam-5300	86	3	+	+	CCONJ
ejpam-5300	86	4	x3	x3	ADJ
ejpam-5300	86	5	+	+	CCONJ
ejpam-5300	86	6	y1	y1	NOUN
ejpam-5300	86	7	−	−	PROPN
ejpam-5300	86	8	x2	x2	PROPN
ejpam-5300	86	9	)	)	PUNCT
ejpam-5300	86	10	·	·	PUNCT
ejpam-5300	86	11	(	(	PUNCT
ejpam-5300	86	12	x3	x3	VERB
ejpam-5300	86	13	+	+	CCONJ
ejpam-5300	86	14	y2	y2	NOUN
ejpam-5300	86	15	)	)	PUNCT
ejpam-5300	86	16	=	=	PRON
ejpam-5300	86	17	(	(	PUNCT
ejpam-5300	86	18	s1	s1	PROPN
ejpam-5300	86	19	−	−	PROPN
ejpam-5300	86	20	x2)(s2	x2)(s2	PUNCT
ejpam-5300	87	1	−	−	PROPN
ejpam-5300	87	2	y1	y1	PROPN
ejpam-5300	87	3	)	)	PUNCT
ejpam-5300	87	4	therefore	therefore	ADV
ejpam-5300	87	5	,	,	PUNCT
ejpam-5300	87	6	ab2	ab2	NOUN
ejpam-5300	87	7	=	=	SYM
ejpam-5300	87	8	√	√	PROPN
ejpam-5300	87	9	(	(	PUNCT
ejpam-5300	87	10	s1	s1	PROPN
ejpam-5300	87	11	−	−	PROPN
ejpam-5300	87	12	x2)(s2	x2)(s2	PUNCT
ejpam-5300	88	1	−	−	PROPN
ejpam-5300	88	2	y1	y1	PROPN
ejpam-5300	88	3	)	)	PUNCT
ejpam-5300	88	4	consider	consider	VERB
ejpam-5300	88	5	a	a	DET
ejpam-5300	88	6	triangle	triangle	NOUN
ejpam-5300	88	7	∆ac1b1	∆ac1b1	NOUN
ejpam-5300	88	8	,	,	PUNCT
ejpam-5300	88	9	where	where	SCONJ
ejpam-5300	88	10	a	a	DET
ejpam-5300	88	11	bisector	bisector	NOUN
ejpam-5300	88	12	line	line	NOUN
ejpam-5300	88	13	is	be	AUX
ejpam-5300	88	14	drawn	draw	VERB
ejpam-5300	88	15	from	from	ADP
ejpam-5300	88	16	vertex	vertex	NOUN
ejpam-5300	88	17	a	a	PRON
ejpam-5300	88	18	to	to	ADP
ejpam-5300	88	19	the	the	DET
ejpam-5300	88	20	opposite	opposite	ADJ
ejpam-5300	88	21	side	side	NOUN
ejpam-5300	88	22	.	.	PUNCT
ejpam-5300	89	1	within	within	ADP
ejpam-5300	89	2	this	this	DET
ejpam-5300	89	3	configuration	configuration	NOUN
ejpam-5300	89	4	,	,	PUNCT
ejpam-5300	89	5	we	we	PRON
ejpam-5300	89	6	explored	explore	VERB
ejpam-5300	89	7	this	this	DET
ejpam-5300	89	8	condition	condition	NOUN
ejpam-5300	89	9	that	that	PRON
ejpam-5300	89	10	used	use	VERB
ejpam-5300	89	11	to	to	PART
ejpam-5300	89	12	describe	describe	VERB
ejpam-5300	89	13	two	two	NUM
ejpam-5300	89	14	circles	circle	NOUN
ejpam-5300	89	15	that	that	PRON
ejpam-5300	89	16	are	be	AUX
ejpam-5300	89	17	tangent	tangent	ADJ
ejpam-5300	89	18	to	to	ADP
ejpam-5300	89	19	each	each	DET
ejpam-5300	89	20	other	other	ADJ
ejpam-5300	89	21	and	and	CCONJ
ejpam-5300	89	22	tangent	tangent	NOUN
ejpam-5300	89	23	to	to	ADP
ejpam-5300	89	24	two	two	NUM
ejpam-5300	89	25	sides	side	NOUN
ejpam-5300	89	26	of	of	ADP
ejpam-5300	89	27	the	the	DET
ejpam-5300	89	28	triangle	triangle	NOUN
ejpam-5300	89	29	with	with	ADP
ejpam-5300	89	30	the	the	DET
ejpam-5300	89	31	bisector	bisector	NOUN
ejpam-5300	89	32	line	line	NOUN
ejpam-5300	89	33	.	.	PUNCT
ejpam-5300	90	1	corollary	corollary	ADJ
ejpam-5300	90	2	2	2	NUM
ejpam-5300	90	3	(	(	PUNCT
ejpam-5300	90	4	triangle	triangle	NOUN
ejpam-5300	90	5	angle	angle	NOUN
ejpam-5300	90	6	bisector	bisector	NOUN
ejpam-5300	90	7	scenario	scenario	PROPN
ejpam-5300	90	8	)	)	PUNCT
ejpam-5300	90	9	consider	consider	VERB
ejpam-5300	90	10	a	a	DET
ejpam-5300	90	11	triangle	triangle	NOUN
ejpam-5300	90	12	∆ab1c1	∆ab1c1	NOUN
ejpam-5300	90	13	with	with	ADP
ejpam-5300	90	14	vertices	vertex	NOUN
ejpam-5300	90	15	a	a	PRON
ejpam-5300	90	16	,	,	PUNCT
ejpam-5300	90	17	b1	b1	NOUN
ejpam-5300	90	18	,	,	PUNCT
ejpam-5300	90	19	and	and	CCONJ
ejpam-5300	90	20	c1	c1	PROPN
ejpam-5300	90	21	.	.	PUNCT
ejpam-5300	91	1	inside	inside	ADP
ejpam-5300	91	2	this	this	DET
ejpam-5300	91	3	triangle	triangle	NOUN
ejpam-5300	91	4	,	,	PUNCT
ejpam-5300	91	5	there	there	PRON
ejpam-5300	91	6	are	be	VERB
ejpam-5300	91	7	two	two	NUM
ejpam-5300	91	8	circles	circle	NOUN
ejpam-5300	91	9	.	.	PUNCT
ejpam-5300	92	1	let	let	VERB
ejpam-5300	92	2	the	the	DET
ejpam-5300	92	3	circles	circle	NOUN
ejpam-5300	92	4	o1	o1	NOUN
ejpam-5300	92	5	(	(	PUNCT
ejpam-5300	92	6	green	green	ADJ
ejpam-5300	92	7	)	)	PUNCT
ejpam-5300	92	8	and	and	CCONJ
ejpam-5300	92	9	o2	o2	PROPN
ejpam-5300	92	10	(	(	PUNCT
ejpam-5300	92	11	blue	blue	ADJ
ejpam-5300	92	12	)	)	PUNCT
ejpam-5300	92	13	as	as	ADP
ejpam-5300	92	14	the	the	DET
ejpam-5300	92	15	incircles	incircle	NOUN
ejpam-5300	92	16	of	of	ADP
ejpam-5300	92	17	the	the	DET
ejpam-5300	92	18	triangles	triangle	NOUN
ejpam-5300	92	19	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	92	20	and	and	CCONJ
ejpam-5300	92	21	∆ac1b2	∆ac1b2	VERB
ejpam-5300	92	22	with	with	ADP
ejpam-5300	92	23	radii	radius	NOUN
ejpam-5300	92	24	r1	r1	NOUN
ejpam-5300	92	25	and	and	CCONJ
ejpam-5300	92	26	r2	r2	PROPN
ejpam-5300	92	27	respectively	respectively	ADV
ejpam-5300	92	28	.	.	PUNCT
ejpam-5300	93	1	circle	circle	PROPN
ejpam-5300	93	2	o1	o1	PROPN
ejpam-5300	93	3	is	be	AUX
ejpam-5300	93	4	tangent	tangent	NOUN
ejpam-5300	93	5	to	to	ADP
ejpam-5300	93	6	the	the	DET
ejpam-5300	93	7	sides	side	NOUN
ejpam-5300	93	8	ab1	ab1	ADV
ejpam-5300	93	9	,	,	PUNCT
ejpam-5300	93	10	ab2	ab2	NOUN
ejpam-5300	93	11	and	and	CCONJ
ejpam-5300	93	12	b1c1	b1c1	PROPN
ejpam-5300	93	13	at	at	ADP
ejpam-5300	93	14	points	point	NOUN
ejpam-5300	93	15	f1	f1	NOUN
ejpam-5300	93	16	,	,	PUNCT
ejpam-5300	93	17	e1	e1	NOUN
ejpam-5300	93	18	,	,	PUNCT
ejpam-5300	93	19	and	and	CCONJ
ejpam-5300	93	20	d1	d1	NOUN
ejpam-5300	93	21	respectively	respectively	ADV
ejpam-5300	93	22	,	,	PUNCT
ejpam-5300	93	23	and	and	CCONJ
ejpam-5300	93	24	circle	circle	NOUN
ejpam-5300	93	25	o2	o2	PROPN
ejpam-5300	93	26	is	be	AUX
ejpam-5300	93	27	tangent	tangent	NOUN
ejpam-5300	93	28	to	to	ADP
ejpam-5300	93	29	the	the	DET
ejpam-5300	93	30	sides	side	NOUN
ejpam-5300	93	31	ac1	ac1	PROPN
ejpam-5300	93	32	,	,	PUNCT
ejpam-5300	93	33	ab2	ab2	ADJ
ejpam-5300	93	34	,	,	PUNCT
ejpam-5300	93	35	and	and	CCONJ
ejpam-5300	94	1	b2c2	b2c2	ADP
ejpam-5300	94	2	at	at	ADP
ejpam-5300	94	3	points	point	NOUN
ejpam-5300	94	4	e2	e2	PROPN
ejpam-5300	94	5	,	,	PUNCT
ejpam-5300	94	6	f2	f2	PROPN
ejpam-5300	94	7	and	and	CCONJ
ejpam-5300	94	8	d2	d2	PROPN
ejpam-5300	94	9	respectively	respectively	ADV
ejpam-5300	94	10	such	such	ADJ
ejpam-5300	94	11	that	that	SCONJ
ejpam-5300	94	12	the	the	DET
ejpam-5300	94	13	following	follow	VERB
ejpam-5300	94	14	conditions	condition	NOUN
ejpam-5300	94	15	hold	hold	VERB
ejpam-5300	94	16	:	:	PUNCT
ejpam-5300	94	17	(	(	PUNCT
ejpam-5300	94	18	i	i	NOUN
ejpam-5300	94	19	)	)	PUNCT
ejpam-5300	94	20	∠b1ab2	∠b1ab2	PROPN
ejpam-5300	95	1	=	=	PUNCT
ejpam-5300	95	2	∠c1ab2	∠c1ab2	PROPN
ejpam-5300	95	3	=	=	SYM
ejpam-5300	95	4	θ	θ	PROPN
ejpam-5300	95	5	(	(	PUNCT
ejpam-5300	95	6	ii	ii	NOUN
ejpam-5300	95	7	)	)	PUNCT
ejpam-5300	95	8	the	the	DET
ejpam-5300	95	9	cevian	cevian	ADJ
ejpam-5300	95	10	ab2	ab2	ADJ
ejpam-5300	95	11	internal	internal	ADJ
ejpam-5300	95	12	bisects	bisect	NOUN
ejpam-5300	95	13	the	the	DET
ejpam-5300	95	14	angle	angle	NOUN
ejpam-5300	95	15	∠b1ac1	∠b1ac1	PROPN
ejpam-5300	95	16	p.	p.	NOUN
ejpam-5300	95	17	boonsomchua	boonsomchua	PROPN
ejpam-5300	95	18	/	/	SYM
ejpam-5300	95	19	eur	eur	PROPN
ejpam-5300	95	20	.	.	PUNCT
ejpam-5300	96	1	j.	j.	PROPN
ejpam-5300	96	2	pure	pure	PROPN
ejpam-5300	96	3	appl	appl	PROPN
ejpam-5300	96	4	.	.	PROPN
ejpam-5300	96	5	math	math	PROPN
ejpam-5300	96	6	,	,	PUNCT
ejpam-5300	96	7	17	17	NUM
ejpam-5300	96	8	(	(	PUNCT
ejpam-5300	96	9	4	4	NUM
ejpam-5300	96	10	)	)	PUNCT
ejpam-5300	96	11	(	(	PUNCT
ejpam-5300	96	12	2024	2024	NUM
ejpam-5300	96	13	)	)	PUNCT
ejpam-5300	96	14	,	,	PUNCT
ejpam-5300	96	15	4135	4135	NUM
ejpam-5300	96	16	-	-	SYM
ejpam-5300	96	17	4146	4146	NUM
ejpam-5300	96	18	4140	4140	NUM
ejpam-5300	96	19	and	and	CCONJ
ejpam-5300	96	20	then	then	ADV
ejpam-5300	96	21	,	,	PUNCT
ejpam-5300	96	22	s2	s2	VERB
ejpam-5300	96	23	−	−	NOUN
ejpam-5300	96	24	y1	y1	NOUN
ejpam-5300	96	25	s2	s2	NOUN
ejpam-5300	96	26	−	−	NOUN
ejpam-5300	96	27	x3	x3	NOUN
ejpam-5300	96	28	=	=	SYM
ejpam-5300	96	29	s1	s1	PROPN
ejpam-5300	96	30	−	−	PROPN
ejpam-5300	96	31	x2	x2	PROPN
ejpam-5300	96	32	s1	s1	PROPN
ejpam-5300	96	33	−	−	PROPN
ejpam-5300	97	1	(	(	PUNCT
ejpam-5300	97	2	x3	x3	VERB
ejpam-5300	97	3	+	+	CCONJ
ejpam-5300	97	4	y1	y1	NOUN
ejpam-5300	97	5	−	−	PROPN
ejpam-5300	97	6	x2	x2	NOUN
ejpam-5300	97	7	)	)	PUNCT
ejpam-5300	97	8	figure	figure	NOUN
ejpam-5300	97	9	7	7	NUM
ejpam-5300	97	10	:	:	PUNCT
ejpam-5300	97	11	the	the	DET
ejpam-5300	97	12	image	image	NOUN
ejpam-5300	97	13	depicts	depict	VERB
ejpam-5300	97	14	the	the	DET
ejpam-5300	97	15	sangaku	sangaku	NOUN
ejpam-5300	97	16	two	two	NUM
ejpam-5300	97	17	circles	circle	NOUN
ejpam-5300	97	18	problem	problem	NOUN
ejpam-5300	97	19	,	,	PUNCT
ejpam-5300	97	20	illustrating	illustrate	VERB
ejpam-5300	97	21	the	the	DET
ejpam-5300	97	22	angle	angle	NOUN
ejpam-5300	97	23	-	-	PUNCT
ejpam-5300	97	24	bisecting	bisecting	NOUN
ejpam-5300	97	25	scenario	scenario	NOUN
ejpam-5300	97	26	.	.	PUNCT
ejpam-5300	98	1	proof	proof	NOUN
ejpam-5300	98	2	.	.	PUNCT
ejpam-5300	99	1	according	accord	VERB
ejpam-5300	99	2	to	to	ADP
ejpam-5300	99	3	the	the	DET
ejpam-5300	99	4	angle	angle	NOUN
ejpam-5300	99	5	-	-	PUNCT
ejpam-5300	99	6	bisector	bisector	NOUN
ejpam-5300	99	7	theorem	theorem	NOUN
ejpam-5300	99	8	in	in	ADP
ejpam-5300	99	9	the	the	DET
ejpam-5300	99	10	triangle	triangle	NOUN
ejpam-5300	99	11	∆ab1c1	∆ab1c1	VERB
ejpam-5300	99	12	so	so	SCONJ
ejpam-5300	99	13	that	that	SCONJ
ejpam-5300	99	14	x1	x1	PROPN
ejpam-5300	100	1	+	+	NUM
ejpam-5300	100	2	x2	x2	PROPN
ejpam-5300	100	3	y1	y1	PROPN
ejpam-5300	100	4	+	+	CCONJ
ejpam-5300	100	5	y2	y2	NOUN
ejpam-5300	100	6	=	=	SYM
ejpam-5300	101	1	x1	x1	PROPN
ejpam-5300	102	1	+	+	CCONJ
ejpam-5300	102	2	x3	x3	ADJ
ejpam-5300	102	3	+	+	CCONJ
ejpam-5300	102	4	y1	y1	NOUN
ejpam-5300	102	5	−	−	PROPN
ejpam-5300	103	1	x2	x2	NOUN
ejpam-5300	103	2	x3	x3	PROPN
ejpam-5300	103	3	+	+	CCONJ
ejpam-5300	104	1	y2	y2	INTJ
ejpam-5300	104	2	therefore	therefore	ADV
ejpam-5300	104	3	,	,	PUNCT
ejpam-5300	104	4	s2	s2	VERB
ejpam-5300	104	5	−	−	NOUN
ejpam-5300	104	6	y1	y1	NOUN
ejpam-5300	104	7	s2	s2	NOUN
ejpam-5300	104	8	−	−	NOUN
ejpam-5300	104	9	x3	x3	NOUN
ejpam-5300	104	10	=	=	SYM
ejpam-5300	104	11	s1	s1	PROPN
ejpam-5300	104	12	−	−	PROPN
ejpam-5300	104	13	x2	x2	PROPN
ejpam-5300	104	14	s1	s1	PROPN
ejpam-5300	104	15	−	−	PROPN
ejpam-5300	105	1	(	(	PUNCT
ejpam-5300	105	2	x3	x3	VERB
ejpam-5300	105	3	+	+	CCONJ
ejpam-5300	105	4	y1	y1	NOUN
ejpam-5300	105	5	−	−	PROPN
ejpam-5300	105	6	x2	x2	PROPN
ejpam-5300	105	7	)	)	PUNCT
ejpam-5300	105	8	the	the	DET
ejpam-5300	105	9	next	next	ADJ
ejpam-5300	105	10	section	section	NOUN
ejpam-5300	105	11	is	be	AUX
ejpam-5300	105	12	inspired	inspire	VERB
ejpam-5300	105	13	by	by	ADP
ejpam-5300	105	14	the	the	DET
ejpam-5300	105	15	american	american	ADJ
ejpam-5300	105	16	invitational	invitational	PROPN
ejpam-5300	105	17	mathematics	mathematics	PROPN
ejpam-5300	105	18	examination	examination	NOUN
ejpam-5300	105	19	2018	2018	NUM
ejpam-5300	105	20	problem	problem	NOUN
ejpam-5300	105	21	13	13	NUM
ejpam-5300	105	22	[	[	PUNCT
ejpam-5300	105	23	see	see	VERB
ejpam-5300	105	24	also	also	ADV
ejpam-5300	105	25	[	[	X
ejpam-5300	105	26	1	1	NUM
ejpam-5300	105	27	]	]	X
ejpam-5300	105	28	]	]	X
ejpam-5300	105	29	as	as	ADP
ejpam-5300	105	30	a	a	DET
ejpam-5300	105	31	technical	technical	ADJ
ejpam-5300	105	32	report	report	NOUN
ejpam-5300	105	33	.	.	PUNCT
ejpam-5300	106	1	this	this	DET
ejpam-5300	106	2	problem	problem	NOUN
ejpam-5300	106	3	is	be	AUX
ejpam-5300	106	4	the	the	DET
ejpam-5300	106	5	best	good	ADJ
ejpam-5300	106	6	sample	sample	NOUN
ejpam-5300	106	7	to	to	PART
ejpam-5300	106	8	point	point	VERB
ejpam-5300	106	9	out	out	ADP
ejpam-5300	106	10	the	the	DET
ejpam-5300	106	11	extended	extended	ADJ
ejpam-5300	106	12	scope	scope	NOUN
ejpam-5300	106	13	of	of	ADP
ejpam-5300	106	14	this	this	DET
ejpam-5300	106	15	study	study	NOUN
ejpam-5300	106	16	.	.	PUNCT
ejpam-5300	107	1	however	however	ADV
ejpam-5300	107	2	,	,	PUNCT
ejpam-5300	107	3	it	it	PRON
ejpam-5300	107	4	obtained	obtain	VERB
ejpam-5300	107	5	a	a	DET
ejpam-5300	107	6	new	new	ADJ
ejpam-5300	107	7	mathematical	mathematical	ADJ
ejpam-5300	107	8	formulation	formulation	NOUN
ejpam-5300	107	9	that	that	PRON
ejpam-5300	107	10	can	can	AUX
ejpam-5300	107	11	describe	describe	VERB
ejpam-5300	107	12	the	the	DET
ejpam-5300	107	13	minimum	minimum	ADJ
ejpam-5300	107	14	area	area	NOUN
ejpam-5300	107	15	of	of	ADP
ejpam-5300	107	16	a	a	DET
ejpam-5300	107	17	triangle	triangle	NOUN
ejpam-5300	107	18	,	,	PUNCT
ejpam-5300	107	19	which	which	PRON
ejpam-5300	107	20	contains	contain	VERB
ejpam-5300	107	21	two	two	NUM
ejpam-5300	107	22	incircles	incircle	NOUN
ejpam-5300	107	23	centered	center	VERB
ejpam-5300	107	24	in	in	ADP
ejpam-5300	107	25	the	the	DET
ejpam-5300	107	26	base	base	NOUN
ejpam-5300	107	27	of	of	ADP
ejpam-5300	107	28	the	the	DET
ejpam-5300	107	29	triangle	triangle	NOUN
ejpam-5300	107	30	.	.	PUNCT
ejpam-5300	108	1	the	the	DET
ejpam-5300	108	2	relation	relation	NOUN
ejpam-5300	108	3	can	can	AUX
ejpam-5300	108	4	be	be	AUX
ejpam-5300	108	5	expressed	express	VERB
ejpam-5300	108	6	in	in	ADP
ejpam-5300	108	7	the	the	DET
ejpam-5300	108	8	form	form	NOUN
ejpam-5300	108	9	of	of	ADP
ejpam-5300	108	10	trigonometry	trigonometry	NOUN
ejpam-5300	108	11	.	.	PUNCT
ejpam-5300	109	1	corollary	corollary	ADJ
ejpam-5300	109	2	3	3	NUM
ejpam-5300	109	3	(	(	PUNCT
ejpam-5300	109	4	area	area	NOUN
ejpam-5300	109	5	minimum	minimum	NOUN
ejpam-5300	109	6	on	on	ADP
ejpam-5300	109	7	bisecting	bisecting	NOUN
ejpam-5300	109	8	triangle	triangle	NOUN
ejpam-5300	109	9	angle	angle	PROPN
ejpam-5300	109	10	scenario	scenario	PROPN
ejpam-5300	109	11	)	)	PUNCT
ejpam-5300	109	12	consider	consider	VERB
ejpam-5300	109	13	a	a	DET
ejpam-5300	109	14	triangle	triangle	NOUN
ejpam-5300	109	15	△	△	X
ejpam-5300	109	16	ab1c1	ab1c1	X
ejpam-5300	109	17	with	with	ADP
ejpam-5300	109	18	vertices	vertex	NOUN
ejpam-5300	109	19	a	a	PRON
ejpam-5300	109	20	,	,	PUNCT
ejpam-5300	109	21	b1	b1	NOUN
ejpam-5300	109	22	,	,	PUNCT
ejpam-5300	109	23	and	and	CCONJ
ejpam-5300	109	24	c1	c1	PROPN
ejpam-5300	109	25	.	.	PUNCT
ejpam-5300	110	1	inside	inside	ADP
ejpam-5300	110	2	this	this	DET
ejpam-5300	110	3	triangle	triangle	NOUN
ejpam-5300	110	4	,	,	PUNCT
ejpam-5300	110	5	there	there	PRON
ejpam-5300	110	6	are	be	VERB
ejpam-5300	110	7	two	two	NUM
ejpam-5300	110	8	circles	circle	NOUN
ejpam-5300	110	9	.	.	PUNCT
ejpam-5300	111	1	denote	denote	VERB
ejpam-5300	111	2	the	the	DET
ejpam-5300	111	3	circles	circle	NOUN
ejpam-5300	111	4	o1	o1	NOUN
ejpam-5300	111	5	(	(	PUNCT
ejpam-5300	111	6	green	green	ADJ
ejpam-5300	111	7	)	)	PUNCT
ejpam-5300	111	8	and	and	CCONJ
ejpam-5300	111	9	o2	o2	PROPN
ejpam-5300	111	10	(	(	PUNCT
ejpam-5300	111	11	blue	blue	ADJ
ejpam-5300	111	12	)	)	PUNCT
ejpam-5300	111	13	as	as	ADP
ejpam-5300	111	14	the	the	DET
ejpam-5300	111	15	incircles	incircle	NOUN
ejpam-5300	111	16	of	of	ADP
ejpam-5300	111	17	the	the	DET
ejpam-5300	111	18	triangles	triangle	NOUN
ejpam-5300	111	19	∆ab1b2	∆ab1b2	NOUN
ejpam-5300	111	20	and	and	CCONJ
ejpam-5300	111	21	∆ac1b2	∆ac1b2	VERB
ejpam-5300	111	22	with	with	ADP
ejpam-5300	111	23	radii	radius	NOUN
ejpam-5300	111	24	r1	r1	NOUN
ejpam-5300	111	25	and	and	CCONJ
ejpam-5300	111	26	r2	r2	PROPN
ejpam-5300	111	27	respectively	respectively	ADV
ejpam-5300	111	28	.	.	PUNCT
ejpam-5300	112	1	circle	circle	PROPN
ejpam-5300	112	2	o1	o1	PROPN
ejpam-5300	112	3	is	be	AUX
ejpam-5300	112	4	tangent	tangent	NOUN
ejpam-5300	112	5	to	to	ADP
ejpam-5300	112	6	the	the	DET
ejpam-5300	112	7	sides	side	NOUN
ejpam-5300	112	8	ab1	ab1	ADV
ejpam-5300	112	9	,	,	PUNCT
ejpam-5300	112	10	ab2	ab2	NOUN
ejpam-5300	112	11	and	and	CCONJ
ejpam-5300	112	12	b1c1	b1c1	PROPN
ejpam-5300	112	13	at	at	ADP
ejpam-5300	112	14	points	point	NOUN
ejpam-5300	112	15	f1	f1	NOUN
ejpam-5300	112	16	,	,	PUNCT
ejpam-5300	112	17	e1	e1	NOUN
ejpam-5300	112	18	,	,	PUNCT
ejpam-5300	112	19	and	and	CCONJ
ejpam-5300	112	20	d1	d1	NOUN
ejpam-5300	112	21	respectively	respectively	ADV
ejpam-5300	112	22	,	,	PUNCT
ejpam-5300	112	23	and	and	CCONJ
ejpam-5300	112	24	circle	circle	NOUN
ejpam-5300	112	25	o2	o2	PROPN
ejpam-5300	112	26	is	be	AUX
ejpam-5300	112	27	tangent	tangent	NOUN
ejpam-5300	112	28	to	to	ADP
ejpam-5300	112	29	the	the	DET
ejpam-5300	112	30	sides	side	NOUN
ejpam-5300	112	31	ac1	ac1	PROPN
ejpam-5300	112	32	,	,	PUNCT
ejpam-5300	112	33	ab2	ab2	ADJ
ejpam-5300	112	34	,	,	PUNCT
ejpam-5300	112	35	and	and	CCONJ
ejpam-5300	113	1	b2c2	b2c2	ADP
ejpam-5300	113	2	at	at	ADP
ejpam-5300	113	3	points	point	NOUN
ejpam-5300	113	4	e2	e2	PROPN
ejpam-5300	113	5	,	,	PUNCT
ejpam-5300	113	6	f2	f2	PROPN
ejpam-5300	113	7	and	and	CCONJ
ejpam-5300	113	8	d2	d2	PROPN
ejpam-5300	113	9	respectively	respectively	ADV
ejpam-5300	113	10	such	such	ADJ
ejpam-5300	113	11	that	that	SCONJ
ejpam-5300	113	12	the	the	DET
ejpam-5300	113	13	following	follow	VERB
ejpam-5300	113	14	conditions	condition	NOUN
ejpam-5300	113	15	hold	hold	VERB
ejpam-5300	113	16	:	:	PUNCT
ejpam-5300	113	17	(	(	PUNCT
ejpam-5300	113	18	i	i	NOUN
ejpam-5300	113	19	)	)	PUNCT
ejpam-5300	113	20	the	the	DET
ejpam-5300	113	21	cevian	cevian	ADJ
ejpam-5300	113	22	ab2	ab2	ADJ
ejpam-5300	113	23	internal	internal	ADJ
ejpam-5300	113	24	bisects	bisect	NOUN
ejpam-5300	113	25	the	the	DET
ejpam-5300	113	26	angle	angle	NOUN
ejpam-5300	113	27	∠b1ac1	∠b1ac1	PROPN
ejpam-5300	113	28	and	and	CCONJ
ejpam-5300	113	29	the	the	DET
ejpam-5300	113	30	angle	angle	NOUN
ejpam-5300	114	1	∠i1ai2	∠i1ai2	PROPN
ejpam-5300	114	2	.	.	PUNCT
ejpam-5300	115	1	and	and	CCONJ
ejpam-5300	115	2	then	then	ADV
ejpam-5300	115	3	,	,	PUNCT
ejpam-5300	115	4	the	the	DET
ejpam-5300	115	5	minimum	minimum	ADJ
ejpam-5300	115	6	area	area	NOUN
ejpam-5300	115	7	of	of	ADP
ejpam-5300	115	8	the	the	DET
ejpam-5300	115	9	triangle	triangle	NOUN
ejpam-5300	116	1	ai1i2	ai1i2	PROPN
ejpam-5300	116	2	is	be	AUX
ejpam-5300	116	3	:	:	PUNCT
ejpam-5300	116	4	(	(	PUNCT
ejpam-5300	116	5	s−	s−	PROPN
ejpam-5300	116	6	a)(s−	a)(s−	PRON
ejpam-5300	116	7	b)(s−	b)(s−	VERB
ejpam-5300	116	8	c	c	NOUN
ejpam-5300	116	9	)	)	PUNCT
ejpam-5300	116	10	a	a	DET
ejpam-5300	116	11	proof	proof	NOUN
ejpam-5300	116	12	.	.	PUNCT
ejpam-5300	117	1	assume	assume	VERB
ejpam-5300	117	2	that	that	SCONJ
ejpam-5300	117	3	the	the	DET
ejpam-5300	117	4	angle	angle	NOUN
ejpam-5300	117	5	∠ab2b1	∠ab2b1	NOUN
ejpam-5300	117	6	=	=	SYM
ejpam-5300	117	7	δ	δ	PROPN
ejpam-5300	117	8	,	,	PUNCT
ejpam-5300	117	9	and	and	CCONJ
ejpam-5300	117	10	that	that	SCONJ
ejpam-5300	117	11	we	we	PRON
ejpam-5300	117	12	have	have	AUX
ejpam-5300	117	13	drawn	draw	VERB
ejpam-5300	117	14	bi1	bi1	NOUN
ejpam-5300	117	15	and	and	CCONJ
ejpam-5300	117	16	ci2	ci2	PROPN
ejpam-5300	117	17	,	,	PUNCT
ejpam-5300	117	18	which	which	PRON
ejpam-5300	117	19	bisect	bisect	VERB
ejpam-5300	117	20	the	the	DET
ejpam-5300	117	21	angles	angle	NOUN
ejpam-5300	117	22	∠ab1c1	∠ab1c1	PUNCT
ejpam-5300	117	23	and	and	CCONJ
ejpam-5300	117	24	∠ac1b1	∠ac1b1	VERB
ejpam-5300	117	25	respectively	respectively	ADV
ejpam-5300	117	26	.	.	PUNCT
ejpam-5300	118	1	∡ab1i1	∡ab1i1	PROPN
ejpam-5300	119	1	=	=	PUNCT
ejpam-5300	120	1	∡i1b1c1	∡i1b1c1	NOUN
ejpam-5300	120	2	=	=	SYM
ejpam-5300	120	3	b	b	PROPN
ejpam-5300	120	4	2	2	NUM
ejpam-5300	120	5	,	,	PUNCT
ejpam-5300	120	6	∡ac1i2	∡ac1i2	X
ejpam-5300	120	7	=	=	PUNCT
ejpam-5300	121	1	∡i2c1b1	∡i2c1b1	PUNCT
ejpam-5300	121	2	=	=	PUNCT
ejpam-5300	121	3	c	c	NOUN
ejpam-5300	121	4	2	2	NUM
ejpam-5300	121	5	,	,	PUNCT
ejpam-5300	121	6	∡ai1b1	∡ai1b1	NOUN
ejpam-5300	121	7	=	=	SYM
ejpam-5300	121	8	90	90	NUM
ejpam-5300	121	9	◦	◦	NOUN
ejpam-5300	121	10	+	+	CCONJ
ejpam-5300	121	11	δ	δ	PROPN
ejpam-5300	121	12	2	2	NUM
ejpam-5300	121	13	,	,	PUNCT
ejpam-5300	121	14	p.	p.	NOUN
ejpam-5300	121	15	boonsomchua	boonsomchua	PROPN
ejpam-5300	121	16	/	/	SYM
ejpam-5300	121	17	eur	eur	PROPN
ejpam-5300	121	18	.	.	PUNCT
ejpam-5300	122	1	j.	j.	PROPN
ejpam-5300	122	2	pure	pure	PROPN
ejpam-5300	122	3	appl	appl	PROPN
ejpam-5300	122	4	.	.	PROPN
ejpam-5300	122	5	math	math	PROPN
ejpam-5300	122	6	,	,	PUNCT
ejpam-5300	122	7	17	17	NUM
ejpam-5300	122	8	(	(	PUNCT
ejpam-5300	122	9	4	4	NUM
ejpam-5300	122	10	)	)	PUNCT
ejpam-5300	122	11	(	(	PUNCT
ejpam-5300	122	12	2024	2024	NUM
ejpam-5300	122	13	)	)	PUNCT
ejpam-5300	122	14	,	,	PUNCT
ejpam-5300	122	15	4135	4135	NUM
ejpam-5300	122	16	-	-	SYM
ejpam-5300	122	17	4146	4146	NUM
ejpam-5300	122	18	4141	4141	NUM
ejpam-5300	122	19	figure	figure	NOUN
ejpam-5300	122	20	8	8	NUM
ejpam-5300	122	21	:	:	PUNCT
ejpam-5300	122	22	this	this	DET
ejpam-5300	122	23	image	image	NOUN
ejpam-5300	122	24	presents	present	VERB
ejpam-5300	122	25	the	the	DET
ejpam-5300	122	26	line	line	NOUN
ejpam-5300	122	27	ab2	ab2	NOUN
ejpam-5300	122	28	internally	internally	ADV
ejpam-5300	122	29	bisecting	bisect	VERB
ejpam-5300	122	30	the	the	DET
ejpam-5300	122	31	angles	angle	NOUN
ejpam-5300	122	32	∠b1ac1	∠b1ac1	PROPN
ejpam-5300	122	33	and	and	CCONJ
ejpam-5300	122	34	∠i1ai2	∠i1ai2	PROPN
ejpam-5300	122	35	.	.	PROPN
ejpam-5300	122	36	figure	figure	NOUN
ejpam-5300	122	37	9	9	NUM
ejpam-5300	122	38	:	:	PUNCT
ejpam-5300	122	39	this	this	DET
ejpam-5300	122	40	image	image	NOUN
ejpam-5300	122	41	illustrates	illustrate	VERB
ejpam-5300	122	42	multiple	multiple	ADJ
ejpam-5300	122	43	lines	line	NOUN
ejpam-5300	122	44	bisecting	bisect	VERB
ejpam-5300	122	45	angles	angle	NOUN
ejpam-5300	122	46	within	within	ADP
ejpam-5300	122	47	this	this	DET
ejpam-5300	122	48	configuration	configuration	NOUN
ejpam-5300	122	49	.	.	PUNCT
ejpam-5300	123	1	∡ab2c1	∡ab2c1	NOUN
ejpam-5300	123	2	=	=	NOUN
ejpam-5300	124	1	180	180	NUM
ejpam-5300	124	2	◦	◦	NOUN
ejpam-5300	124	3	−	−	PROPN
ejpam-5300	124	4	δ	δ	PROPN
ejpam-5300	124	5	,	,	PUNCT
ejpam-5300	124	6	∡ai2c1	∡ai2c1	PROPN
ejpam-5300	124	7	=	=	NOUN
ejpam-5300	124	8	180	180	NUM
ejpam-5300	124	9	◦	◦	NOUN
ejpam-5300	124	10	−	−	NOUN
ejpam-5300	124	11	δ	δ	NOUN
ejpam-5300	124	12	2	2	NUM
ejpam-5300	124	13	,	,	PUNCT
ejpam-5300	124	14	∡i1ai2	∡i1ai2	NOUN
ejpam-5300	124	15	=	=	PUNCT
ejpam-5300	124	16	α+	α+	PUNCT
ejpam-5300	124	17	β	β	X
ejpam-5300	124	18	next	next	ADV
ejpam-5300	124	19	,	,	PUNCT
ejpam-5300	124	20	using	use	VERB
ejpam-5300	124	21	the	the	DET
ejpam-5300	124	22	sine	sine	ADJ
ejpam-5300	124	23	law	law	NOUN
ejpam-5300	124	24	is	be	AUX
ejpam-5300	124	25	important	important	ADJ
ejpam-5300	124	26	for	for	ADP
ejpam-5300	124	27	deriving	derive	VERB
ejpam-5300	124	28	relationships	relationship	NOUN
ejpam-5300	124	29	between	between	ADP
ejpam-5300	124	30	the	the	DET
ejpam-5300	124	31	sides	side	NOUN
ejpam-5300	124	32	of	of	ADP
ejpam-5300	124	33	the	the	DET
ejpam-5300	124	34	triangle	triangle	NOUN
ejpam-5300	124	35	and	and	CCONJ
ejpam-5300	124	36	the	the	DET
ejpam-5300	124	37	relevant	relevant	ADJ
ejpam-5300	124	38	angles	angle	NOUN
ejpam-5300	124	39	in	in	ADP
ejpam-5300	124	40	this	this	DET
ejpam-5300	124	41	configuration	configuration	NOUN
ejpam-5300	124	42	:	:	PUNCT
ejpam-5300	124	43	ai1	ai1	X
ejpam-5300	124	44	=	=	PUNCT
ejpam-5300	124	45	sin	sin	NOUN
ejpam-5300	124	46	(	(	PUNCT
ejpam-5300	124	47	b	b	NOUN
ejpam-5300	124	48	2	2	X
ejpam-5300	124	49	)	)	PUNCT
ejpam-5300	124	50	sin	sin	NOUN
ejpam-5300	124	51	(	(	PUNCT
ejpam-5300	124	52	90	90	NUM
ejpam-5300	124	53	◦	◦	NOUN
ejpam-5300	124	54	+	+	CCONJ
ejpam-5300	124	55	δ	δ	NOUN
ejpam-5300	124	56	2	2	NUM
ejpam-5300	124	57	)	)	PUNCT
ejpam-5300	124	58	·	·	PUNCT
ejpam-5300	125	1	c	c	X
ejpam-5300	125	2	(	(	PUNCT
ejpam-5300	125	3	5	5	NUM
ejpam-5300	125	4	)	)	PUNCT
ejpam-5300	125	5	ai2	ai2	NOUN
ejpam-5300	125	6	=	=	NOUN
ejpam-5300	125	7	sin	sin	NOUN
ejpam-5300	125	8	(	(	PUNCT
ejpam-5300	125	9	c	c	NOUN
ejpam-5300	125	10	2	2	NUM
ejpam-5300	125	11	)	)	PUNCT
ejpam-5300	125	12	sin	sin	NOUN
ejpam-5300	125	13	(	(	PUNCT
ejpam-5300	125	14	180	180	NUM
ejpam-5300	125	15	◦	◦	NOUN
ejpam-5300	125	16	−	−	NOUN
ejpam-5300	125	17	δ	δ	NOUN
ejpam-5300	125	18	2	2	NUM
ejpam-5300	125	19	)	)	PUNCT
ejpam-5300	125	20	·	·	PUNCT
ejpam-5300	126	1	b	b	X
ejpam-5300	126	2	(	(	PUNCT
ejpam-5300	126	3	6	6	NUM
ejpam-5300	126	4	)	)	PUNCT
ejpam-5300	126	5	substituting	substitute	VERB
ejpam-5300	126	6	the	the	DET
ejpam-5300	126	7	equation	equation	NOUN
ejpam-5300	126	8	(	(	PUNCT
ejpam-5300	126	9	5	5	NUM
ejpam-5300	126	10	)	)	PUNCT
ejpam-5300	126	11	and	and	CCONJ
ejpam-5300	126	12	(	(	PUNCT
ejpam-5300	126	13	6	6	NUM
ejpam-5300	126	14	)	)	PUNCT
ejpam-5300	126	15	into	into	ADP
ejpam-5300	126	16	the	the	DET
ejpam-5300	126	17	area	area	NOUN
ejpam-5300	126	18	of	of	ADP
ejpam-5300	126	19	triangle	triangle	NOUN
ejpam-5300	126	20	trigonometry	trigonometry	NOUN
ejpam-5300	126	21	formulation	formulation	NOUN
ejpam-5300	126	22	.	.	PUNCT
ejpam-5300	127	1	[	[	X
ejpam-5300	127	2	ai1i2	ai1i2	X
ejpam-5300	127	3	]	]	X
ejpam-5300	127	4	=	=	SYM
ejpam-5300	127	5	1	1	NUM
ejpam-5300	127	6	2	2	NUM
ejpam-5300	127	7	·	·	PUNCT
ejpam-5300	127	8	ai1	ai1	X
ejpam-5300	127	9	·	·	SYM
ejpam-5300	127	10	ai2	ai2	X
ejpam-5300	127	11	·	·	PUNCT
ejpam-5300	127	12	sin	sin	NOUN
ejpam-5300	127	13	(	(	PUNCT
ejpam-5300	127	14	a	a	DET
ejpam-5300	127	15	2	2	NUM
ejpam-5300	127	16	)	)	PUNCT
ejpam-5300	127	17	=	=	SYM
ejpam-5300	127	18	1	1	NUM
ejpam-5300	127	19	2	2	NUM
ejpam-5300	127	20	·	·	SYM
ejpam-5300	127	21	b	b	X
ejpam-5300	127	22	·	·	PUNCT
ejpam-5300	127	23	c	c	X
ejpam-5300	127	24	·	·	PUNCT
ejpam-5300	127	25	sin	sin	NOUN
ejpam-5300	127	26	(	(	PUNCT
ejpam-5300	127	27	a	a	DET
ejpam-5300	127	28	2	2	NUM
ejpam-5300	127	29	)	)	PUNCT
ejpam-5300	127	30	·	·	PUNCT
ejpam-5300	127	31	sin	sin	NOUN
ejpam-5300	127	32	(	(	PUNCT
ejpam-5300	127	33	b	b	NOUN
ejpam-5300	127	34	2	2	NUM
ejpam-5300	127	35	)	)	PUNCT
ejpam-5300	127	36	·	·	PUNCT
ejpam-5300	127	37	sin	sin	NOUN
ejpam-5300	127	38	(	(	PUNCT
ejpam-5300	127	39	c	c	NOUN
ejpam-5300	127	40	2	2	X
ejpam-5300	127	41	)	)	PUNCT
ejpam-5300	127	42	sin	sin	NOUN
ejpam-5300	127	43	(	(	PUNCT
ejpam-5300	128	1	90	90	NUM
ejpam-5300	128	2	◦	◦	NOUN
ejpam-5300	128	3	+	+	CCONJ
ejpam-5300	128	4	δ	δ	NOUN
ejpam-5300	128	5	2	2	NUM
ejpam-5300	128	6	)	)	PUNCT
ejpam-5300	128	7	·	·	PUNCT
ejpam-5300	128	8	sin	sin	NOUN
ejpam-5300	128	9	(	(	PUNCT
ejpam-5300	128	10	180	180	NUM
ejpam-5300	128	11	◦	◦	NOUN
ejpam-5300	128	12	−	−	NOUN
ejpam-5300	128	13	δ	δ	NOUN
ejpam-5300	128	14	2	2	NUM
ejpam-5300	128	15	)	)	PUNCT
ejpam-5300	128	16	and	and	CCONJ
ejpam-5300	128	17	then	then	ADV
ejpam-5300	128	18	,	,	PUNCT
ejpam-5300	128	19	[	[	X
ejpam-5300	128	20	ai1i2	ai1i2	X
ejpam-5300	128	21	]	]	X
ejpam-5300	128	22	=	=	SYM
ejpam-5300	128	23	b	b	X
ejpam-5300	128	24	·	·	PUNCT
ejpam-5300	128	25	c	c	X
ejpam-5300	128	26	·	·	PUNCT
ejpam-5300	128	27	sin(a2	sin(a2	NOUN
ejpam-5300	128	28	)	)	PUNCT
ejpam-5300	128	29	·	·	PUNCT
ejpam-5300	128	30	sin	sin	NOUN
ejpam-5300	128	31	(	(	PUNCT
ejpam-5300	128	32	b	b	NOUN
ejpam-5300	128	33	2	2	NUM
ejpam-5300	128	34	)	)	PUNCT
ejpam-5300	128	35	·	·	PUNCT
ejpam-5300	128	36	sin	sin	NOUN
ejpam-5300	128	37	(	(	PUNCT
ejpam-5300	128	38	c	c	NOUN
ejpam-5300	128	39	2	2	X
ejpam-5300	128	40	)	)	PUNCT
ejpam-5300	128	41	sin	sin	NOUN
ejpam-5300	128	42	δ	δ	PROPN
ejpam-5300	128	43	noting	note	VERB
ejpam-5300	128	44	that	that	SCONJ
ejpam-5300	128	45	1	1	NUM
ejpam-5300	128	46	≤	≤	NUM
ejpam-5300	128	47	1	1	NUM
ejpam-5300	128	48	sin	sin	NOUN
ejpam-5300	128	49	δ	δ	PROPN
ejpam-5300	128	50	and	and	CCONJ
ejpam-5300	128	51	sin(a2	sin(a2	VERB
ejpam-5300	128	52	)	)	PUNCT
ejpam-5300	129	1	=	=	PUNCT
ejpam-5300	129	2	±	±	NOUN
ejpam-5300	129	3	√	√	NOUN
ejpam-5300	129	4	1−cosa	1−cosa	NUM
ejpam-5300	129	5	2	2	NUM
ejpam-5300	129	6	.	.	PUNCT
ejpam-5300	130	1	we	we	PRON
ejpam-5300	130	2	deduce	deduce	VERB
ejpam-5300	130	3	the	the	DET
ejpam-5300	130	4	minimum	minimum	ADJ
ejpam-5300	130	5	area	area	NOUN
ejpam-5300	130	6	of	of	ADP
ejpam-5300	130	7	triangle	triangle	NOUN
ejpam-5300	130	8	ai1i2	ai1i2	PROPN
ejpam-5300	130	9	from	from	ADP
ejpam-5300	130	10	the	the	DET
ejpam-5300	130	11	following	follow	VERB
ejpam-5300	130	12	inequality	inequality	NOUN
ejpam-5300	130	13	establishes	establish	VERB
ejpam-5300	130	14	a	a	DET
ejpam-5300	130	15	lower	low	ADJ
ejpam-5300	130	16	bound	bind	VERB
ejpam-5300	130	17	.	.	PUNCT
ejpam-5300	131	1	[	[	X
ejpam-5300	131	2	ai1i2	ai1i2	X
ejpam-5300	131	3	]	]	X
ejpam-5300	131	4	≥	≥	X
ejpam-5300	131	5	b	b	X
ejpam-5300	131	6	·	·	PUNCT
ejpam-5300	131	7	c	c	X
ejpam-5300	131	8	·	·	PUNCT
ejpam-5300	131	9	(	(	PUNCT
ejpam-5300	131	10	√	√	NUM
ejpam-5300	131	11	(	(	PUNCT
ejpam-5300	131	12	1−	1−	NUM
ejpam-5300	131	13	cosa)(1−	cosa)(1−	PROPN
ejpam-5300	131	14	cosb)(1−	cosb)(1−	PROPN
ejpam-5300	131	15	cosc	cosc	NOUN
ejpam-5300	131	16	)	)	PUNCT
ejpam-5300	131	17	8	8	NUM
ejpam-5300	131	18	)	)	PUNCT
ejpam-5300	131	19	(	(	PUNCT
ejpam-5300	131	20	7	7	X
ejpam-5300	131	21	)	)	PUNCT
ejpam-5300	131	22	we	we	PRON
ejpam-5300	131	23	applied	apply	VERB
ejpam-5300	131	24	the	the	DET
ejpam-5300	131	25	law	law	NOUN
ejpam-5300	131	26	of	of	ADP
ejpam-5300	131	27	cosines	cosine	NOUN
ejpam-5300	131	28	to	to	ADP
ejpam-5300	131	29	the	the	DET
ejpam-5300	131	30	concyclic	concyclic	NOUN
ejpam-5300	131	31	angles	angle	NOUN
ejpam-5300	131	32	.	.	PUNCT
ejpam-5300	132	1	this	this	PRON
ejpam-5300	132	2	is	be	AUX
ejpam-5300	132	3	an	an	DET
ejpam-5300	132	4	important	important	ADJ
ejpam-5300	132	5	point	point	NOUN
ejpam-5300	132	6	because	because	SCONJ
ejpam-5300	132	7	it	it	PRON
ejpam-5300	132	8	reduces	reduce	VERB
ejpam-5300	132	9	the	the	DET
ejpam-5300	132	10	trigonometric	trigonometric	ADJ
ejpam-5300	132	11	calculations	calculation	NOUN
ejpam-5300	132	12	involving	involve	VERB
ejpam-5300	132	13	cosines	cosine	NOUN
ejpam-5300	132	14	to	to	ADP
ejpam-5300	132	15	a	a	DET
ejpam-5300	132	16	relationship	relationship	NOUN
ejpam-5300	132	17	between	between	ADP
ejpam-5300	132	18	the	the	DET
ejpam-5300	132	19	sides	side	NOUN
ejpam-5300	132	20	of	of	ADP
ejpam-5300	132	21	the	the	DET
ejpam-5300	132	22	triangle	triangle	NOUN
ejpam-5300	132	23	.	.	PUNCT
ejpam-5300	133	1	1−	1−	NUM
ejpam-5300	133	2	cosa	cosa	NOUN
ejpam-5300	133	3	=	=	SYM
ejpam-5300	133	4	(	(	PUNCT
ejpam-5300	133	5	a−	a−	PROPN
ejpam-5300	133	6	b+	b+	ADJ
ejpam-5300	133	7	c)(a+	c)(a+	NOUN
ejpam-5300	133	8	b−	b−	NOUN
ejpam-5300	133	9	c	c	PROPN
ejpam-5300	133	10	)	)	PUNCT
ejpam-5300	133	11	2bc	2bc	NOUN
ejpam-5300	133	12	,	,	PUNCT
ejpam-5300	133	13	(	(	PUNCT
ejpam-5300	133	14	8)	8)	NUM
ejpam-5300	133	15	1−	1−	NUM
ejpam-5300	133	16	cosb	cosb	NOUN
ejpam-5300	133	17	=	=	SYM
ejpam-5300	133	18	(	(	PUNCT
ejpam-5300	133	19	b+	b+	X
ejpam-5300	133	20	c−	c−	ADJ
ejpam-5300	133	21	a)(b+	a)(b+	NOUN
ejpam-5300	133	22	a−	a−	PROPN
ejpam-5300	133	23	c	c	NOUN
ejpam-5300	133	24	)	)	PUNCT
ejpam-5300	133	25	2ca	2ca	NOUN
ejpam-5300	133	26	,	,	PUNCT
ejpam-5300	133	27	(	(	PUNCT
ejpam-5300	133	28	9	9	NUM
ejpam-5300	133	29	)	)	PUNCT
ejpam-5300	133	30	1−	1−	NUM
ejpam-5300	133	31	cosc	cosc	NOUN
ejpam-5300	133	32	=	=	PUNCT
ejpam-5300	133	33	(	(	PUNCT
ejpam-5300	133	34	b+	b+	X
ejpam-5300	133	35	c−	c−	ADJ
ejpam-5300	133	36	a)(a+	a)(a+	NOUN
ejpam-5300	133	37	c−	c−	ADJ
ejpam-5300	133	38	b	b	NOUN
ejpam-5300	133	39	)	)	PUNCT
ejpam-5300	133	40	2ab	2ab	NOUN
ejpam-5300	133	41	.	.	PUNCT
ejpam-5300	134	1	(	(	PUNCT
ejpam-5300	134	2	10	10	NUM
ejpam-5300	134	3	)	)	PUNCT
ejpam-5300	134	4	p.	p.	NOUN
ejpam-5300	134	5	boonsomchua	boonsomchua	PROPN
ejpam-5300	134	6	/	/	SYM
ejpam-5300	134	7	eur	eur	PROPN
ejpam-5300	134	8	.	.	PUNCT
ejpam-5300	135	1	j.	j.	PROPN
ejpam-5300	135	2	pure	pure	PROPN
ejpam-5300	135	3	appl	appl	PROPN
ejpam-5300	135	4	.	.	PROPN
ejpam-5300	135	5	math	math	PROPN
ejpam-5300	135	6	,	,	PUNCT
ejpam-5300	135	7	17	17	NUM
ejpam-5300	135	8	(	(	PUNCT
ejpam-5300	135	9	4	4	NUM
ejpam-5300	135	10	)	)	PUNCT
ejpam-5300	135	11	(	(	PUNCT
ejpam-5300	135	12	2024	2024	NUM
ejpam-5300	135	13	)	)	PUNCT
ejpam-5300	135	14	,	,	PUNCT
ejpam-5300	135	15	4135	4135	NUM
ejpam-5300	135	16	-	-	SYM
ejpam-5300	135	17	4146	4146	NUM
ejpam-5300	135	18	4142	4142	NUM
ejpam-5300	135	19	substituting	substitute	VERB
ejpam-5300	135	20	equations	equation	NOUN
ejpam-5300	135	21	(	(	PUNCT
ejpam-5300	135	22	8)	8)	NUM
ejpam-5300	135	23	,	,	PUNCT
ejpam-5300	135	24	(	(	PUNCT
ejpam-5300	135	25	9	9	NUM
ejpam-5300	135	26	)	)	PUNCT
ejpam-5300	135	27	,	,	PUNCT
ejpam-5300	135	28	and	and	CCONJ
ejpam-5300	135	29	(	(	PUNCT
ejpam-5300	135	30	10	10	NUM
ejpam-5300	135	31	)	)	PUNCT
ejpam-5300	135	32	into	into	ADP
ejpam-5300	135	33	equation	equation	NOUN
ejpam-5300	135	34	(	(	PUNCT
ejpam-5300	135	35	7	7	NUM
ejpam-5300	135	36	)	)	PUNCT
ejpam-5300	135	37	.	.	PUNCT
ejpam-5300	136	1	therefore	therefore	ADV
ejpam-5300	136	2	,	,	PUNCT
ejpam-5300	136	3	the	the	DET
ejpam-5300	136	4	minimum	minimum	ADJ
ejpam-5300	136	5	area	area	NOUN
ejpam-5300	136	6	of	of	ADP
ejpam-5300	136	7	the	the	DET
ejpam-5300	136	8	triangle	triangle	NOUN
ejpam-5300	136	9	ai1i2	ai1i2	PROPN
ejpam-5300	136	10	is	be	AUX
ejpam-5300	136	11	:	:	PUNCT
ejpam-5300	136	12	(	(	PUNCT
ejpam-5300	136	13	s−	s−	PROPN
ejpam-5300	136	14	a)(s−	a)(s−	PRON
ejpam-5300	136	15	b)(s−	b)(s−	VERB
ejpam-5300	136	16	c	c	NOUN
ejpam-5300	136	17	)	)	PUNCT
ejpam-5300	136	18	a	a	DET
ejpam-5300	136	19	section	section	NOUN
ejpam-5300	136	20	2	2	NUM
ejpam-5300	136	21	generalization	generalization	NOUN
ejpam-5300	136	22	of	of	ADP
ejpam-5300	136	23	angela	angela	PROPN
ejpam-5300	136	24	drei	drei	PROPN
ejpam-5300	136	25	’s	’s	PART
ejpam-5300	136	26	proof	proof	NOUN
ejpam-5300	136	27	-	-	PUNCT
ejpam-5300	136	28	inspired	inspire	VERB
ejpam-5300	136	29	analysis	analysis	NOUN
ejpam-5300	136	30	of	of	ADP
ejpam-5300	136	31	inclusion	inclusion	NOUN
ejpam-5300	136	32	inin	inin	VERB
ejpam-5300	136	33	a	a	DET
ejpam-5300	136	34	sectorial	sectorial	ADJ
ejpam-5300	136	35	triangular	triangular	NOUN
ejpam-5300	136	36	configuration	configuration	NOUN
ejpam-5300	136	37	theorem	theorem	NOUN
ejpam-5300	136	38	2	2	NUM
ejpam-5300	136	39	let	let	VERB
ejpam-5300	136	40	a	a	DET
ejpam-5300	136	41	triangle	triangle	NOUN
ejpam-5300	136	42	△	△	PUNCT
ejpam-5300	136	43	ab1bn+1	ab1bn+1	VERB
ejpam-5300	136	44	with	with	ADP
ejpam-5300	136	45	rays	ray	NOUN
ejpam-5300	136	46	abu	abu	PROPN
ejpam-5300	136	47	from	from	ADP
ejpam-5300	136	48	vertex	vertex	NOUN
ejpam-5300	136	49	a.	a.	NOUN
ejpam-5300	136	50	for	for	ADP
ejpam-5300	136	51	u	u	PROPN
ejpam-5300	136	52	∈	∈	PROPN
ejpam-5300	136	53	{	{	PUNCT
ejpam-5300	136	54	1	1	NUM
ejpam-5300	136	55	,	,	PUNCT
ejpam-5300	136	56	.	.	PUNCT
ejpam-5300	136	57	.	.	PUNCT
ejpam-5300	136	58	.	.	PUNCT
ejpam-5300	136	59	,	,	PUNCT
ejpam-5300	136	60	n	n	CCONJ
ejpam-5300	136	61	}	}	PUNCT
ejpam-5300	136	62	,	,	PUNCT
ejpam-5300	136	63	suppose	suppose	VERB
ejpam-5300	136	64	that	that	SCONJ
ejpam-5300	136	65	ou	ou	PROPN
ejpam-5300	136	66	is	be	AUX
ejpam-5300	136	67	the	the	DET
ejpam-5300	136	68	u	u	PROPN
ejpam-5300	136	69	-	-	PUNCT
ejpam-5300	136	70	th	th	VERB
ejpam-5300	136	71	inscribed	inscribe	VERB
ejpam-5300	136	72	circle	circle	NOUN
ejpam-5300	136	73	with	with	ADP
ejpam-5300	136	74	radii	radius	NOUN
ejpam-5300	136	75	ru	ru	NOUN
ejpam-5300	136	76	in	in	ADP
ejpam-5300	136	77	the	the	DET
ejpam-5300	136	78	triangle	triangle	NOUN
ejpam-5300	136	79	abubu+1	abubu+1	PROPN
ejpam-5300	136	80	.	.	PUNCT
ejpam-5300	137	1	it	it	PRON
ejpam-5300	137	2	holds	hold	VERB
ejpam-5300	137	3	that	that	SCONJ
ejpam-5300	137	4	ou	ou	PROPN
ejpam-5300	137	5	is	be	AUX
ejpam-5300	137	6	touch	touch	NOUN
ejpam-5300	137	7	to	to	ADP
ejpam-5300	137	8	abu	abu	PROPN
ejpam-5300	137	9	,	,	PUNCT
ejpam-5300	137	10	abu+1	abu+1	NOUN
ejpam-5300	137	11	,	,	PUNCT
ejpam-5300	137	12	and	and	CCONJ
ejpam-5300	137	13	bubu+1	bubu+1	NOUN
ejpam-5300	137	14	at	at	ADP
ejpam-5300	137	15	fu	fu	PROPN
ejpam-5300	137	16	,	,	PUNCT
ejpam-5300	137	17	eu	eu	PROPN
ejpam-5300	137	18	and	and	CCONJ
ejpam-5300	137	19	du	du	X
ejpam-5300	137	20	respectively	respectively	ADV
ejpam-5300	137	21	.	.	PUNCT
ejpam-5300	138	1	given	give	VERB
ejpam-5300	138	2	the	the	DET
ejpam-5300	138	3	lengths	length	NOUN
ejpam-5300	138	4	aeu	aeu	ADV
ejpam-5300	138	5	,	,	PUNCT
ejpam-5300	138	6	and	and	CCONJ
ejpam-5300	138	7	afu	afu	PROPN
ejpam-5300	138	8	be	be	AUX
ejpam-5300	138	9	xu	xu	PROPN
ejpam-5300	138	10	,	,	PUNCT
ejpam-5300	138	11	and	and	CCONJ
ejpam-5300	138	12	yu	yu	PROPN
ejpam-5300	138	13	respectively	respectively	ADV
ejpam-5300	138	14	,	,	PUNCT
ejpam-5300	138	15	where	where	SCONJ
ejpam-5300	138	16	su	su	PROPN
ejpam-5300	138	17	is	be	AUX
ejpam-5300	138	18	the	the	DET
ejpam-5300	138	19	semi	semi	ADJ
ejpam-5300	138	20	-	-	NOUN
ejpam-5300	138	21	parameter	parameter	NOUN
ejpam-5300	138	22	of	of	ADP
ejpam-5300	138	23	triangle	triangle	NOUN
ejpam-5300	138	24	abubu+1	abubu+1	PROPN
ejpam-5300	138	25	.	.	PUNCT
ejpam-5300	139	1	then	then	ADV
ejpam-5300	139	2	,	,	PUNCT
ejpam-5300	139	3	r1	r1	PROPN
ejpam-5300	139	4	rn	rn	PROPN
ejpam-5300	139	5	=	=	PROPN
ejpam-5300	139	6	sn	sn	PROPN
ejpam-5300	139	7	s1	s1	PROPN
ejpam-5300	139	8	·	·	PUNCT
ejpam-5300	139	9	n∏	n∏	NOUN
ejpam-5300	139	10	i=2	i=2	PROPN
ejpam-5300	139	11	(	(	PUNCT
ejpam-5300	139	12	si−1	si−1	PROPN
ejpam-5300	139	13	−	−	PROPN
ejpam-5300	139	14	xi	xi	ADP
ejpam-5300	139	15	si	si	PROPN
ejpam-5300	139	16	−	−	PROPN
ejpam-5300	139	17	yi−1	yi−1	PROPN
ejpam-5300	139	18	)	)	PUNCT
ejpam-5300	139	19	figure	figure	NOUN
ejpam-5300	139	20	10	10	NUM
ejpam-5300	139	21	:	:	PUNCT
ejpam-5300	139	22	the	the	DET
ejpam-5300	139	23	image	image	NOUN
ejpam-5300	139	24	illustrates	illustrate	VERB
ejpam-5300	139	25	the	the	DET
ejpam-5300	139	26	approach	approach	NOUN
ejpam-5300	139	27	to	to	ADP
ejpam-5300	139	28	the	the	DET
ejpam-5300	139	29	generalized	generalize	VERB
ejpam-5300	139	30	sangaku	sangaku	NOUN
ejpam-5300	139	31	problem	problem	NOUN
ejpam-5300	139	32	for	for	ADP
ejpam-5300	139	33	n	n	DET
ejpam-5300	139	34	-circles	-circle	NOUN
ejpam-5300	139	35	.	.	PUNCT
ejpam-5300	140	1	proof	proof	NOUN
ejpam-5300	140	2	.	.	PUNCT
ejpam-5300	141	1	consider	consider	VERB
ejpam-5300	141	2	the	the	DET
ejpam-5300	141	3	statement	statement	NOUN
ejpam-5300	141	4	p	p	NOUN
ejpam-5300	141	5	(	(	PUNCT
ejpam-5300	141	6	n	n	CCONJ
ejpam-5300	141	7	)	)	PUNCT
ejpam-5300	141	8	defined	define	VERB
ejpam-5300	141	9	as	as	ADP
ejpam-5300	141	10	:	:	PUNCT
ejpam-5300	141	11	p	p	X
ejpam-5300	141	12	(	(	PUNCT
ejpam-5300	141	13	n	n	CCONJ
ejpam-5300	141	14	)	)	PUNCT
ejpam-5300	141	15	=	=	PUNCT
ejpam-5300	141	16	rn−1	rn−1	PROPN
ejpam-5300	141	17	rn	rn	PROPN
ejpam-5300	141	18	=	=	PROPN
ejpam-5300	141	19	sn	sn	PROPN
ejpam-5300	141	20	sn−1	sn−1	PROPN
ejpam-5300	141	21	·	·	PUNCT
ejpam-5300	141	22	(	(	PUNCT
ejpam-5300	141	23	sn−1	sn−1	PROPN
ejpam-5300	141	24	−	−	PROPN
ejpam-5300	141	25	xn	xn	PROPN
ejpam-5300	141	26	sn	sn	PROPN
ejpam-5300	142	1	−	−	PROPN
ejpam-5300	142	2	yn−1	yn−1	INTJ
ejpam-5300	142	3	)	)	PUNCT
ejpam-5300	142	4	(	(	PUNCT
ejpam-5300	142	5	11	11	NUM
ejpam-5300	142	6	)	)	PUNCT
ejpam-5300	142	7	where	where	SCONJ
ejpam-5300	142	8	it	it	PRON
ejpam-5300	142	9	is	be	AUX
ejpam-5300	142	10	known	know	VERB
ejpam-5300	142	11	from	from	ADP
ejpam-5300	142	12	equation	equation	NOUN
ejpam-5300	142	13	(	(	PUNCT
ejpam-5300	142	14	11	11	NUM
ejpam-5300	142	15	)	)	PUNCT
ejpam-5300	143	1	that	that	SCONJ
ejpam-5300	143	2	p	p	X
ejpam-5300	143	3	(	(	PUNCT
ejpam-5300	143	4	n	n	CCONJ
ejpam-5300	143	5	)	)	PUNCT
ejpam-5300	143	6	holds	hold	VERB
ejpam-5300	143	7	true	true	ADJ
ejpam-5300	143	8	for	for	SCONJ
ejpam-5300	143	9	all	all	DET
ejpam-5300	143	10	positive	positive	ADJ
ejpam-5300	143	11	integers	integer	NOUN
ejpam-5300	143	12	n.	n.	NOUN
ejpam-5300	143	13	substituting	substitute	VERB
ejpam-5300	143	14	the	the	DET
ejpam-5300	143	15	values	value	NOUN
ejpam-5300	143	16	from	from	ADP
ejpam-5300	143	17	n	n	NOUN
ejpam-5300	143	18	=	=	SYM
ejpam-5300	143	19	2	2	NUM
ejpam-5300	143	20	to	to	ADP
ejpam-5300	143	21	n	n	NOUN
ejpam-5300	143	22	=	=	SYM
ejpam-5300	143	23	n	n	NOUN
ejpam-5300	143	24	into	into	ADP
ejpam-5300	143	25	the	the	DET
ejpam-5300	143	26	equation	equation	NOUN
ejpam-5300	143	27	,	,	PUNCT
ejpam-5300	143	28	we	we	PRON
ejpam-5300	143	29	obtain	obtain	VERB
ejpam-5300	143	30	:	:	PUNCT
ejpam-5300	143	31	n∏	n∏	PROPN
ejpam-5300	143	32	i=2	i=2	PROPN
ejpam-5300	143	33	p	p	X
ejpam-5300	143	34	(	(	PUNCT
ejpam-5300	143	35	i	i	NOUN
ejpam-5300	143	36	)	)	PUNCT
ejpam-5300	143	37	=	=	PUNCT
ejpam-5300	143	38	(	(	PUNCT
ejpam-5300	143	39	r1	r1	PROPN
ejpam-5300	143	40	r2	r2	PROPN
ejpam-5300	143	41	)	)	PUNCT
ejpam-5300	143	42	(	(	PUNCT
ejpam-5300	143	43	r2	r2	PROPN
ejpam-5300	143	44	r3	r3	PROPN
ejpam-5300	143	45	)	)	PUNCT
ejpam-5300	143	46	·	·	PUNCT
ejpam-5300	143	47	·	·	PUNCT
ejpam-5300	143	48	·	·	PUNCT
ejpam-5300	143	49	(	(	PUNCT
ejpam-5300	143	50	rn−1	rn−1	PROPN
ejpam-5300	143	51	rn	rn	PROPN
ejpam-5300	143	52	)	)	PUNCT
ejpam-5300	143	53	=	=	PUNCT
ejpam-5300	143	54	(	(	PUNCT
ejpam-5300	143	55	s2	s2	NOUN
ejpam-5300	143	56	s1	s1	NOUN
ejpam-5300	143	57	)	)	PUNCT
ejpam-5300	143	58	(	(	PUNCT
ejpam-5300	143	59	s3	s3	PROPN
ejpam-5300	143	60	s2	s2	PROPN
ejpam-5300	143	61	)	)	PUNCT
ejpam-5300	143	62	·	·	PUNCT
ejpam-5300	143	63	·	·	PUNCT
ejpam-5300	143	64	·	·	PUNCT
ejpam-5300	143	65	(	(	PUNCT
ejpam-5300	143	66	sn	sn	INTJ
ejpam-5300	143	67	sn−1	sn−1	PROPN
ejpam-5300	143	68	)	)	PUNCT
ejpam-5300	143	69	·	·	PUNCT
ejpam-5300	143	70	n∏	n∏	NOUN
ejpam-5300	143	71	i=2	i=2	PROPN
ejpam-5300	143	72	(	(	PUNCT
ejpam-5300	143	73	si−1	si−1	PROPN
ejpam-5300	143	74	−	−	PROPN
ejpam-5300	143	75	xi	xi	ADP
ejpam-5300	143	76	si	si	PROPN
ejpam-5300	143	77	−	−	PROPN
ejpam-5300	143	78	yi−1	yi−1	PROPN
ejpam-5300	143	79	)	)	PUNCT
ejpam-5300	143	80	further	far	ADV
ejpam-5300	143	81	simplifying	simplify	VERB
ejpam-5300	143	82	.	.	PUNCT
ejpam-5300	144	1	therefore	therefore	ADV
ejpam-5300	144	2	,	,	PUNCT
ejpam-5300	144	3	p.	p.	NOUN
ejpam-5300	144	4	boonsomchua	boonsomchua	PROPN
ejpam-5300	144	5	/	/	SYM
ejpam-5300	144	6	eur	eur	PROPN
ejpam-5300	144	7	.	.	PUNCT
ejpam-5300	145	1	j.	j.	PROPN
ejpam-5300	145	2	pure	pure	PROPN
ejpam-5300	145	3	appl	appl	PROPN
ejpam-5300	145	4	.	.	PROPN
ejpam-5300	145	5	math	math	PROPN
ejpam-5300	145	6	,	,	PUNCT
ejpam-5300	145	7	17	17	NUM
ejpam-5300	145	8	(	(	PUNCT
ejpam-5300	145	9	4	4	NUM
ejpam-5300	145	10	)	)	PUNCT
ejpam-5300	145	11	(	(	PUNCT
ejpam-5300	145	12	2024	2024	NUM
ejpam-5300	145	13	)	)	PUNCT
ejpam-5300	145	14	,	,	PUNCT
ejpam-5300	145	15	4135	4135	NUM
ejpam-5300	145	16	-	-	SYM
ejpam-5300	145	17	4146	4146	NUM
ejpam-5300	145	18	4143	4143	NUM
ejpam-5300	145	19	r1	r1	PROPN
ejpam-5300	145	20	rn	rn	PROPN
ejpam-5300	145	21	=	=	PROPN
ejpam-5300	145	22	sn	sn	PROPN
ejpam-5300	145	23	s1	s1	PROPN
ejpam-5300	145	24	·	·	PUNCT
ejpam-5300	145	25	n∏	n∏	NOUN
ejpam-5300	145	26	i=2	i=2	PROPN
ejpam-5300	145	27	(	(	PUNCT
ejpam-5300	145	28	si−1	si−1	PROPN
ejpam-5300	145	29	−	−	PROPN
ejpam-5300	145	30	xi	xi	ADP
ejpam-5300	145	31	si	si	PROPN
ejpam-5300	146	1	−	−	PROPN
ejpam-5300	146	2	yi−1	yi−1	PROPN
ejpam-5300	146	3	)	)	PUNCT
ejpam-5300	146	4	remark	remark	NOUN
ejpam-5300	146	5	1	1	NUM
ejpam-5300	146	6	.	.	PUNCT
ejpam-5300	147	1	this	this	PRON
ejpam-5300	147	2	is	be	AUX
ejpam-5300	147	3	a	a	DET
ejpam-5300	147	4	remark	remark	NOUN
ejpam-5300	147	5	about	about	ADP
ejpam-5300	147	6	the	the	DET
ejpam-5300	147	7	telescoping	telescope	VERB
ejpam-5300	147	8	product	product	NOUN
ejpam-5300	147	9	from	from	ADP
ejpam-5300	147	10	equation	equation	NOUN
ejpam-5300	147	11	(	(	PUNCT
ejpam-5300	147	12	x	x	NOUN
ejpam-5300	147	13	)	)	PUNCT
ejpam-5300	147	14	,	,	PUNCT
ejpam-5300	147	15	which	which	PRON
ejpam-5300	147	16	presented	present	VERB
ejpam-5300	147	17	the	the	DET
ejpam-5300	147	18	inscribed	inscribe	VERB
ejpam-5300	147	19	radii	radii	NOUN
ejpam-5300	147	20	fractions	fraction	NOUN
ejpam-5300	147	21	is	be	AUX
ejpam-5300	147	22	shown	show	VERB
ejpam-5300	147	23	,	,	PUNCT
ejpam-5300	147	24	generalized	generalize	VERB
ejpam-5300	147	25	to	to	ADP
ejpam-5300	147	26	the	the	DET
ejpam-5300	147	27	independent	independent	ADJ
ejpam-5300	147	28	variables	variable	NOUN
ejpam-5300	147	29	j	j	PROPN
ejpam-5300	147	30	and	and	CCONJ
ejpam-5300	147	31	k	k	PROPN
ejpam-5300	147	32	for	for	ADP
ejpam-5300	147	33	all	all	DET
ejpam-5300	147	34	j	j	PROPN
ejpam-5300	147	35	,	,	PUNCT
ejpam-5300	147	36	k	k	PROPN
ejpam-5300	147	37	∈	∈	PROPN
ejpam-5300	147	38	{	{	PUNCT
ejpam-5300	147	39	2	2	NUM
ejpam-5300	147	40	,	,	PUNCT
ejpam-5300	147	41	.	.	PUNCT
ejpam-5300	147	42	.	.	PUNCT
ejpam-5300	148	1	.	.	PUNCT
ejpam-5300	148	2	,	,	PUNCT
ejpam-5300	148	3	n	n	CCONJ
ejpam-5300	148	4	}	}	PUNCT
ejpam-5300	148	5	.	.	PUNCT
ejpam-5300	149	1	therefore	therefore	ADV
ejpam-5300	149	2	,	,	PUNCT
ejpam-5300	149	3	rk	rk	NOUN
ejpam-5300	149	4	rj+1	rj+1	NOUN
ejpam-5300	149	5	=	=	NOUN
ejpam-5300	149	6	sj+1	sj+1	PROPN
ejpam-5300	149	7	sk	sk	VERB
ejpam-5300	149	8	·	·	PUNCT
ejpam-5300	149	9	j+1∏	j+1∏	NOUN
ejpam-5300	149	10	o	o	NOUN
ejpam-5300	149	11	=	=	X
ejpam-5300	149	12	k	k	X
ejpam-5300	149	13	(	(	PUNCT
ejpam-5300	149	14	so	so	ADV
ejpam-5300	149	15	−	−	PROPN
ejpam-5300	149	16	xo+1	xo+1	SYM
ejpam-5300	149	17	so+1	so+1	PROPN
ejpam-5300	149	18	−	−	PROPN
ejpam-5300	149	19	yo	yo	PROPN
ejpam-5300	149	20	)	)	PUNCT
ejpam-5300	149	21	.	.	PUNCT
ejpam-5300	150	1	section	section	NOUN
ejpam-5300	150	2	3	3	NUM
ejpam-5300	150	3	generalization	generalization	NOUN
ejpam-5300	150	4	of	of	ADP
ejpam-5300	150	5	angera	angera	PROPN
ejpam-5300	150	6	drei	drei	PROPN
ejpam-5300	150	7	’s	’s	PART
ejpam-5300	150	8	proof	proof	NOUN
ejpam-5300	150	9	-	-	PUNCT
ejpam-5300	150	10	inspired	inspire	VERB
ejpam-5300	150	11	analysis	analysis	NOUN
ejpam-5300	150	12	of	of	ADP
ejpam-5300	150	13	inclusion	inclusion	NOUN
ejpam-5300	150	14	inand	inand	PROPN
ejpam-5300	150	15	ex	ex	NOUN
ejpam-5300	150	16	-	-	NOUN
ejpam-5300	150	17	circles	circle	NOUN
ejpam-5300	150	18	in	in	ADP
ejpam-5300	150	19	a	a	DET
ejpam-5300	150	20	sectorial	sectorial	ADJ
ejpam-5300	150	21	triangular	triangular	NOUN
ejpam-5300	150	22	configuration	configuration	NOUN
ejpam-5300	150	23	theorem	theorem	VERB
ejpam-5300	150	24	3	3	NUM
ejpam-5300	150	25	let	let	VERB
ejpam-5300	150	26	a	a	DET
ejpam-5300	150	27	triangle	triangle	NOUN
ejpam-5300	150	28	△	△	PUNCT
ejpam-5300	150	29	ab1bn+1	ab1bn+1	NOUN
ejpam-5300	150	30	with	with	ADP
ejpam-5300	150	31	extended	extended	ADJ
ejpam-5300	150	32	rays	ray	NOUN
ejpam-5300	150	33	abu	abu	PROPN
ejpam-5300	150	34	from	from	ADP
ejpam-5300	150	35	vertex	vertex	NOUN
ejpam-5300	150	36	a.	a.	NOUN
ejpam-5300	150	37	for	for	ADP
ejpam-5300	150	38	u	u	PROPN
ejpam-5300	150	39	∈	∈	PROPN
ejpam-5300	150	40	{	{	PUNCT
ejpam-5300	150	41	1	1	NUM
ejpam-5300	150	42	,	,	PUNCT
ejpam-5300	150	43	.	.	PUNCT
ejpam-5300	150	44	.	.	PUNCT
ejpam-5300	151	1	.	.	PUNCT
ejpam-5300	152	1	,	,	PUNCT
ejpam-5300	152	2	n	n	CCONJ
ejpam-5300	152	3	}	}	PUNCT
ejpam-5300	152	4	,	,	PUNCT
ejpam-5300	152	5	suppose	suppose	VERB
ejpam-5300	152	6	that	that	SCONJ
ejpam-5300	152	7	ou	ou	PROPN
ejpam-5300	152	8	is	be	AUX
ejpam-5300	152	9	the	the	DET
ejpam-5300	152	10	u	u	PROPN
ejpam-5300	152	11	-	-	PUNCT
ejpam-5300	152	12	th	th	VERB
ejpam-5300	152	13	inscribed	inscribe	VERB
ejpam-5300	152	14	circle	circle	NOUN
ejpam-5300	152	15	with	with	ADP
ejpam-5300	152	16	radii	radius	NOUN
ejpam-5300	152	17	ru	ru	NOUN
ejpam-5300	152	18	in	in	ADP
ejpam-5300	152	19	the	the	DET
ejpam-5300	152	20	triangle	triangle	NOUN
ejpam-5300	152	21	abubu+1	abubu+1	PROPN
ejpam-5300	152	22	,	,	PUNCT
ejpam-5300	152	23	and	and	CCONJ
ejpam-5300	152	24	contains	contain	VERB
ejpam-5300	152	25	o′	o′	PROPN
ejpam-5300	152	26	u	u	NOUN
ejpam-5300	152	27	is	be	AUX
ejpam-5300	152	28	the	the	DET
ejpam-5300	152	29	escribed	escribe	VERB
ejpam-5300	152	30	circle	circle	NOUN
ejpam-5300	152	31	with	with	ADP
ejpam-5300	152	32	radii	radius	NOUN
ejpam-5300	152	33	ru	ru	NOUN
ejpam-5300	152	34	that	that	PRON
ejpam-5300	152	35	are	be	AUX
ejpam-5300	152	36	tangent	tangent	ADJ
ejpam-5300	152	37	to	to	ADP
ejpam-5300	152	38	the	the	DET
ejpam-5300	152	39	common	common	ADJ
ejpam-5300	152	40	base	base	NOUN
ejpam-5300	152	41	bnbn+1	bnbn+1	ADV
ejpam-5300	152	42	by	by	ADP
ejpam-5300	152	43	supposing	suppose	VERB
ejpam-5300	152	44	the	the	DET
ejpam-5300	152	45	angle	angle	NOUN
ejpam-5300	152	46	∠abibi+1	∠abibi+1	PUNCT
ejpam-5300	152	47	is	be	AUX
ejpam-5300	152	48	set	set	VERB
ejpam-5300	152	49	to	to	ADP
ejpam-5300	152	50	bi−1	bi−1	PROPN
ejpam-5300	152	51	.	.	PUNCT
ejpam-5300	153	1	then	then	ADV
ejpam-5300	153	2	,	,	PUNCT
ejpam-5300	153	3	n∏	n∏	PROPN
ejpam-5300	153	4	i=1	i=1	PROPN
ejpam-5300	153	5	ri	ri	PROPN
ejpam-5300	153	6	ri	ri	PROPN
ejpam-5300	153	7	=	=	PROPN
ejpam-5300	153	8	tan	tan	PROPN
ejpam-5300	153	9	(	(	PUNCT
ejpam-5300	153	10	b	b	NOUN
ejpam-5300	153	11	2	2	NUM
ejpam-5300	153	12	)	)	PUNCT
ejpam-5300	153	13	·	·	PUNCT
ejpam-5300	153	14	tan	tan	PROPN
ejpam-5300	153	15	(	(	PUNCT
ejpam-5300	153	16	c	c	NOUN
ejpam-5300	153	17	2	2	X
ejpam-5300	153	18	)	)	PUNCT
ejpam-5300	153	19	figure	figure	NOUN
ejpam-5300	153	20	11	11	NUM
ejpam-5300	153	21	:	:	PUNCT
ejpam-5300	153	22	the	the	DET
ejpam-5300	153	23	image	image	NOUN
ejpam-5300	153	24	illustrates	illustrate	VERB
ejpam-5300	153	25	the	the	DET
ejpam-5300	153	26	approach	approach	NOUN
ejpam-5300	153	27	to	to	ADP
ejpam-5300	153	28	the	the	DET
ejpam-5300	153	29	generalized	generalize	VERB
ejpam-5300	153	30	sangaku	sangaku	NOUN
ejpam-5300	153	31	problem	problem	NOUN
ejpam-5300	153	32	for	for	ADP
ejpam-5300	153	33	n	n	PRON
ejpam-5300	153	34	-inscribe	-inscribe	ADJ
ejpam-5300	153	35	and	and	CCONJ
ejpam-5300	153	36	escribed	escribe	VERB
ejpam-5300	153	37	circles	circle	NOUN
ejpam-5300	153	38	.	.	PUNCT
ejpam-5300	154	1	proof	proof	NOUN
ejpam-5300	154	2	1	1	NUM
ejpam-5300	154	3	.	.	PUNCT
ejpam-5300	155	1	by	by	ADP
ejpam-5300	155	2	trigonometric	trigonometric	ADJ
ejpam-5300	155	3	formulations	formulation	NOUN
ejpam-5300	155	4	for	for	ADP
ejpam-5300	155	5	bisecting	bisecting	NOUN
ejpam-5300	155	6	angles	angle	NOUN
ejpam-5300	155	7	,	,	PUNCT
ejpam-5300	155	8	sin	sin	NOUN
ejpam-5300	155	9	(	(	PUNCT
ejpam-5300	155	10	a	a	DET
ejpam-5300	155	11	2	2	NUM
ejpam-5300	155	12	)	)	PUNCT
ejpam-5300	155	13	=	=	SYM
ejpam-5300	155	14	√	√	PROPN
ejpam-5300	155	15	(	(	PUNCT
ejpam-5300	155	16	s−	s−	PROPN
ejpam-5300	155	17	b)(s−	b)(s−	VERB
ejpam-5300	155	18	c	c	NOUN
ejpam-5300	155	19	)	)	PUNCT
ejpam-5300	155	20	bc	bc	PROPN
ejpam-5300	155	21	,	,	PUNCT
ejpam-5300	155	22	cos	cos	PROPN
ejpam-5300	155	23	(	(	PUNCT
ejpam-5300	155	24	a	a	DET
ejpam-5300	155	25	2	2	NUM
ejpam-5300	155	26	)	)	PUNCT
ejpam-5300	155	27	=	=	SYM
ejpam-5300	155	28	√	√	PROPN
ejpam-5300	155	29	s(s−	s(s−	PROPN
ejpam-5300	155	30	a	a	X
ejpam-5300	155	31	)	)	PUNCT
ejpam-5300	155	32	bc	bc	PROPN
ejpam-5300	155	33	,	,	PUNCT
ejpam-5300	155	34	p.	p.	PROPN
ejpam-5300	155	35	boonsomchua	boonsomchua	PROPN
ejpam-5300	155	36	/	/	SYM
ejpam-5300	155	37	eur	eur	PROPN
ejpam-5300	155	38	.	.	PUNCT
ejpam-5300	156	1	j.	j.	PROPN
ejpam-5300	156	2	pure	pure	PROPN
ejpam-5300	156	3	appl	appl	PROPN
ejpam-5300	156	4	.	.	PROPN
ejpam-5300	156	5	math	math	PROPN
ejpam-5300	156	6	,	,	PUNCT
ejpam-5300	156	7	17	17	NUM
ejpam-5300	156	8	(	(	PUNCT
ejpam-5300	156	9	4	4	NUM
ejpam-5300	156	10	)	)	PUNCT
ejpam-5300	156	11	(	(	PUNCT
ejpam-5300	156	12	2024	2024	NUM
ejpam-5300	156	13	)	)	PUNCT
ejpam-5300	156	14	,	,	PUNCT
ejpam-5300	156	15	4135	4135	NUM
ejpam-5300	156	16	-	-	SYM
ejpam-5300	156	17	4146	4146	NUM
ejpam-5300	156	18	4144	4144	NUM
ejpam-5300	156	19	tan	tan	PROPN
ejpam-5300	156	20	(	(	PUNCT
ejpam-5300	156	21	a	a	DET
ejpam-5300	156	22	2	2	NUM
ejpam-5300	156	23	)	)	PUNCT
ejpam-5300	156	24	=	=	SYM
ejpam-5300	156	25	√	√	PROPN
ejpam-5300	156	26	(	(	PUNCT
ejpam-5300	156	27	s−	s−	PROPN
ejpam-5300	156	28	b)(s−	b)(s−	VERB
ejpam-5300	156	29	c	c	NOUN
ejpam-5300	156	30	)	)	PUNCT
ejpam-5300	156	31	s(s−	s(s−	PROPN
ejpam-5300	156	32	a	a	X
ejpam-5300	156	33	)	)	PUNCT
ejpam-5300	156	34	.	.	PUNCT
ejpam-5300	157	1	applying	apply	VERB
ejpam-5300	157	2	heron	heron	NOUN
ejpam-5300	157	3	’s	’s	PART
ejpam-5300	157	4	formula	formula	NOUN
ejpam-5300	157	5	,	,	PUNCT
ejpam-5300	157	6	the	the	DET
ejpam-5300	157	7	expression	expression	NOUN
ejpam-5300	157	8	can	can	AUX
ejpam-5300	157	9	be	be	AUX
ejpam-5300	157	10	written	write	VERB
ejpam-5300	157	11	as	as	SCONJ
ejpam-5300	157	12	follows	follow	VERB
ejpam-5300	157	13	the	the	DET
ejpam-5300	157	14	relationship	relationship	NOUN
ejpam-5300	157	15	between	between	ADP
ejpam-5300	157	16	any	any	DET
ejpam-5300	157	17	consecutive	consecutive	ADJ
ejpam-5300	157	18	angles	angle	NOUN
ejpam-5300	157	19	b	b	NOUN
ejpam-5300	157	20	is	be	AUX
ejpam-5300	157	21	given	give	VERB
ejpam-5300	157	22	by	by	ADP
ejpam-5300	157	23	:	:	PUNCT
ejpam-5300	157	24	tan	tan	PROPN
ejpam-5300	157	25	(	(	PUNCT
ejpam-5300	157	26	b	b	PROPN
ejpam-5300	157	27	2	2	NUM
ejpam-5300	157	28	)	)	PUNCT
ejpam-5300	157	29	·	·	PUNCT
ejpam-5300	158	1	tan	tan	PROPN
ejpam-5300	158	2	(	(	PUNCT
ejpam-5300	158	3	b1	b1	NOUN
ejpam-5300	158	4	2	2	NUM
ejpam-5300	158	5	)	)	PUNCT
ejpam-5300	158	6	=	=	SYM
ejpam-5300	158	7	√	√	PROPN
ejpam-5300	158	8	(	(	PUNCT
ejpam-5300	158	9	s−b1b2)(s−ab1)(s−ab1)(s−ab2	s−b1b2)(s−ab1)(s−ab1)(s−ab2	PROPN
ejpam-5300	158	10	)	)	PUNCT
ejpam-5300	158	11	s2(s−ab2)(s−b1b2	s2(s−ab2)(s−b1b2	ADJ
ejpam-5300	158	12	)	)	PUNCT
ejpam-5300	159	1	=	=	PROPN
ejpam-5300	159	2	r1	r1	PROPN
ejpam-5300	159	3	r1	r1	PROPN
ejpam-5300	159	4	(	(	PUNCT
ejpam-5300	159	5	12	12	NUM
ejpam-5300	159	6	)	)	PUNCT
ejpam-5300	159	7	similarly	similarly	ADV
ejpam-5300	159	8	,	,	PUNCT
ejpam-5300	159	9	this	this	DET
ejpam-5300	159	10	mathematical	mathematical	ADJ
ejpam-5300	159	11	formulation	formulation	NOUN
ejpam-5300	159	12	allows	allow	VERB
ejpam-5300	159	13	us	we	PRON
ejpam-5300	159	14	to	to	PART
ejpam-5300	159	15	repeat	repeat	VERB
ejpam-5300	159	16	angle	angle	NOUN
ejpam-5300	159	17	terms	term	NOUN
ejpam-5300	159	18	for	for	ADP
ejpam-5300	159	19	each	each	DET
ejpam-5300	159	20	substitution	substitution	NOUN
ejpam-5300	159	21	in	in	ADP
ejpam-5300	159	22	equation	equation	NOUN
ejpam-5300	159	23	(	(	PUNCT
ejpam-5300	159	24	12	12	NUM
ejpam-5300	159	25	):	):	PUNCT
ejpam-5300	159	26	r2	r2	PROPN
ejpam-5300	159	27	r2	r2	PROPN
ejpam-5300	159	28	=	=	SYM
ejpam-5300	159	29	tan	tan	PROPN
ejpam-5300	159	30	(	(	PUNCT
ejpam-5300	159	31	180	180	NUM
ejpam-5300	159	32	◦	◦	NOUN
ejpam-5300	159	33	−b1	−b1	PROPN
ejpam-5300	159	34	2	2	NUM
ejpam-5300	159	35	)	)	PUNCT
ejpam-5300	159	36	·	·	PUNCT
ejpam-5300	159	37	tan	tan	PROPN
ejpam-5300	159	38	(	(	PUNCT
ejpam-5300	159	39	b2	b2	PROPN
ejpam-5300	159	40	2	2	NUM
ejpam-5300	159	41	)	)	PUNCT
ejpam-5300	159	42	,	,	PUNCT
ejpam-5300	159	43	r3	r3	PROPN
ejpam-5300	159	44	r3	r3	PROPN
ejpam-5300	159	45	=	=	PROPN
ejpam-5300	159	46	tan	tan	PROPN
ejpam-5300	159	47	(	(	PUNCT
ejpam-5300	159	48	180	180	NUM
ejpam-5300	159	49	◦	◦	NOUN
ejpam-5300	159	50	−b2	−b2	ADJ
ejpam-5300	159	51	2	2	NUM
ejpam-5300	159	52	)	)	PUNCT
ejpam-5300	159	53	·	·	PUNCT
ejpam-5300	159	54	tan	tan	PROPN
ejpam-5300	159	55	(	(	PUNCT
ejpam-5300	159	56	b3	b3	PROPN
ejpam-5300	159	57	2	2	NUM
ejpam-5300	159	58	)	)	PUNCT
ejpam-5300	159	59	,	,	PUNCT
ejpam-5300	159	60	...	...	PUNCT
ejpam-5300	160	1	rn	rn	PROPN
ejpam-5300	160	2	rn	rn	PROPN
ejpam-5300	161	1	=	=	PROPN
ejpam-5300	161	2	tan	tan	PROPN
ejpam-5300	161	3	(	(	PUNCT
ejpam-5300	161	4	180	180	NUM
ejpam-5300	161	5	◦	◦	NOUN
ejpam-5300	161	6	−bn−1	−bn−1	X
ejpam-5300	161	7	2	2	NUM
ejpam-5300	161	8	)	)	PUNCT
ejpam-5300	161	9	·	·	PUNCT
ejpam-5300	161	10	tan	tan	PROPN
ejpam-5300	161	11	(	(	PUNCT
ejpam-5300	161	12	c	c	NOUN
ejpam-5300	161	13	2	2	NUM
ejpam-5300	161	14	)	)	PUNCT
ejpam-5300	161	15	.	.	PUNCT
ejpam-5300	162	1	upon	upon	SCONJ
ejpam-5300	162	2	multiplying	multiply	VERB
ejpam-5300	162	3	these	these	DET
ejpam-5300	162	4	previous	previous	ADJ
ejpam-5300	162	5	n	n	DET
ejpam-5300	162	6	equations	equation	NOUN
ejpam-5300	162	7	,	,	PUNCT
ejpam-5300	162	8	the	the	DET
ejpam-5300	162	9	final	final	ADJ
ejpam-5300	162	10	product	product	NOUN
ejpam-5300	162	11	is	be	AUX
ejpam-5300	162	12	derived	derive	VERB
ejpam-5300	162	13	as	as	SCONJ
ejpam-5300	162	14	follows	follow	VERB
ejpam-5300	162	15	:	:	PUNCT
ejpam-5300	163	1	n∏	n∏	PROPN
ejpam-5300	163	2	i=1	i=1	PROPN
ejpam-5300	163	3	ri	ri	PROPN
ejpam-5300	163	4	ri	ri	PROPN
ejpam-5300	163	5	=	=	PROPN
ejpam-5300	163	6	tan	tan	PROPN
ejpam-5300	163	7	(	(	PUNCT
ejpam-5300	163	8	b	b	NOUN
ejpam-5300	163	9	2	2	NUM
ejpam-5300	163	10	)	)	PUNCT
ejpam-5300	163	11	·	·	PUNCT
ejpam-5300	163	12	tan	tan	PROPN
ejpam-5300	163	13	(	(	PUNCT
ejpam-5300	163	14	c	c	NOUN
ejpam-5300	163	15	2	2	NUM
ejpam-5300	163	16	)	)	PUNCT
ejpam-5300	163	17	·	·	PUNCT
ejpam-5300	164	1	n−1∏	n−1∏	ADP
ejpam-5300	164	2	i=1	i=1	PROPN
ejpam-5300	164	3	tan	tan	PROPN
ejpam-5300	164	4	(	(	PUNCT
ejpam-5300	164	5	180	180	NUM
ejpam-5300	164	6	◦	◦	NOUN
ejpam-5300	164	7	−bi	−bi	NOUN
ejpam-5300	164	8	2	2	NUM
ejpam-5300	164	9	)	)	PUNCT
ejpam-5300	164	10	and	and	CCONJ
ejpam-5300	164	11	simplifying	simplify	VERB
ejpam-5300	164	12	using	use	VERB
ejpam-5300	164	13	the	the	DET
ejpam-5300	164	14	tangent	tangent	ADJ
ejpam-5300	164	15	identity	identity	NOUN
ejpam-5300	164	16	,	,	PUNCT
ejpam-5300	164	17	we	we	PRON
ejpam-5300	164	18	deduce	deduce	VERB
ejpam-5300	164	19	:	:	PUNCT
ejpam-5300	164	20	n∏	n∏	PROPN
ejpam-5300	164	21	i=1	i=1	PROPN
ejpam-5300	164	22	ri	ri	PROPN
ejpam-5300	164	23	ri	ri	PROPN
ejpam-5300	165	1	=	=	PROPN
ejpam-5300	165	2	tan	tan	PROPN
ejpam-5300	165	3	(	(	PUNCT
ejpam-5300	165	4	b	b	NOUN
ejpam-5300	165	5	2	2	NUM
ejpam-5300	165	6	)	)	PUNCT
ejpam-5300	165	7	·	·	PUNCT
ejpam-5300	165	8	tan	tan	PROPN
ejpam-5300	165	9	(	(	PUNCT
ejpam-5300	165	10	c	c	NOUN
ejpam-5300	165	11	2	2	NUM
ejpam-5300	165	12	)	)	PUNCT
ejpam-5300	165	13	3	3	NUM
ejpam-5300	165	14	.	.	PUNCT
ejpam-5300	165	15	discussions	discussion	NOUN
ejpam-5300	165	16	and	and	CCONJ
ejpam-5300	165	17	conclusions	conclusion	NOUN
ejpam-5300	165	18	by	by	ADP
ejpam-5300	165	19	extending	extend	VERB
ejpam-5300	165	20	the	the	DET
ejpam-5300	165	21	equal	equal	ADJ
ejpam-5300	165	22	incircles	incircle	NOUN
ejpam-5300	165	23	theorem	theorem	VERB
ejpam-5300	165	24	,	,	PUNCT
ejpam-5300	165	25	this	this	DET
ejpam-5300	165	26	paper	paper	NOUN
ejpam-5300	165	27	aims	aim	VERB
ejpam-5300	165	28	to	to	PART
ejpam-5300	165	29	develop	develop	VERB
ejpam-5300	165	30	a	a	DET
ejpam-5300	165	31	mathematical	mathematical	ADJ
ejpam-5300	165	32	framework	framework	NOUN
ejpam-5300	165	33	that	that	PRON
ejpam-5300	165	34	generalizes	generalize	VERB
ejpam-5300	165	35	the	the	DET
ejpam-5300	165	36	multiple	multiple	ADJ
ejpam-5300	165	37	incircles	incircle	NOUN
ejpam-5300	165	38	problem	problem	NOUN
ejpam-5300	165	39	,	,	PUNCT
ejpam-5300	165	40	allowing	allow	VERB
ejpam-5300	165	41	for	for	ADP
ejpam-5300	165	42	non	non	ADJ
ejpam-5300	165	43	-	-	ADJ
ejpam-5300	165	44	equal	equal	ADJ
ejpam-5300	165	45	radii	radius	NOUN
ejpam-5300	165	46	.	.	PUNCT
ejpam-5300	166	1	this	this	DET
ejpam-5300	166	2	study	study	NOUN
ejpam-5300	166	3	enhances	enhance	VERB
ejpam-5300	166	4	the	the	DET
ejpam-5300	166	5	understanding	understanding	NOUN
ejpam-5300	166	6	of	of	ADP
ejpam-5300	166	7	the	the	DET
ejpam-5300	166	8	equal	equal	ADJ
ejpam-5300	166	9	incircles	incircle	NOUN
ejpam-5300	166	10	theorem	theorem	VERB
ejpam-5300	166	11	based	base	VERB
ejpam-5300	166	12	on	on	ADP
ejpam-5300	166	13	the	the	DET
ejpam-5300	166	14	generalized	generalized	ADJ
ejpam-5300	166	15	sangaku	sangaku	NOUN
ejpam-5300	166	16	problem	problem	NOUN
ejpam-5300	166	17	.	.	PUNCT
ejpam-5300	167	1	in	in	ADP
ejpam-5300	167	2	section	section	NOUN
ejpam-5300	167	3	1	1	NUM
ejpam-5300	167	4	,	,	PUNCT
ejpam-5300	167	5	this	this	DET
ejpam-5300	167	6	paper	paper	NOUN
ejpam-5300	167	7	revealed	reveal	VERB
ejpam-5300	167	8	the	the	DET
ejpam-5300	167	9	relationship	relationship	NOUN
ejpam-5300	167	10	between	between	ADP
ejpam-5300	167	11	the	the	DET
ejpam-5300	167	12	fraction	fraction	NOUN
ejpam-5300	167	13	of	of	ADP
ejpam-5300	167	14	sub	sub	NOUN
ejpam-5300	167	15	-	-	NOUN
ejpam-5300	167	16	circles	circle	NOUN
ejpam-5300	167	17	in	in	ADP
ejpam-5300	167	18	terms	term	NOUN
ejpam-5300	167	19	of	of	ADP
ejpam-5300	167	20	trigonometry	trigonometry	NOUN
ejpam-5300	167	21	for	for	ADP
ejpam-5300	167	22	both	both	PRON
ejpam-5300	167	23	initial	initial	ADJ
ejpam-5300	167	24	angles	angle	NOUN
ejpam-5300	167	25	(	(	PUNCT
ejpam-5300	167	26	b	b	NOUN
ejpam-5300	167	27	,	,	PUNCT
ejpam-5300	167	28	c	c	NOUN
ejpam-5300	167	29	)	)	PUNCT
ejpam-5300	167	30	.	.	PUNCT
ejpam-5300	168	1	although	although	SCONJ
ejpam-5300	168	2	the	the	DET
ejpam-5300	168	3	numerator	numerator	NOUN
ejpam-5300	168	4	and	and	CCONJ
ejpam-5300	168	5	denominator	denominator	NOUN
ejpam-5300	168	6	are	be	AUX
ejpam-5300	168	7	similar	similar	ADJ
ejpam-5300	168	8	in	in	ADP
ejpam-5300	168	9	form	form	NOUN
ejpam-5300	168	10	,	,	PUNCT
ejpam-5300	168	11	they	they	PRON
ejpam-5300	168	12	differ	differ	VERB
ejpam-5300	168	13	in	in	ADP
ejpam-5300	168	14	the	the	DET
ejpam-5300	168	15	initial	initial	ADJ
ejpam-5300	168	16	angles	angle	NOUN
ejpam-5300	168	17	and	and	CCONJ
ejpam-5300	168	18	the	the	DET
ejpam-5300	168	19	semi	semi	ADJ
ejpam-5300	168	20	-	-	NOUN
ejpam-5300	168	21	perimeter	perimeter	NOUN
ejpam-5300	168	22	of	of	ADP
ejpam-5300	168	23	the	the	DET
ejpam-5300	168	24	triangle	triangle	NOUN
ejpam-5300	168	25	involving	involve	VERB
ejpam-5300	168	26	two	two	NUM
ejpam-5300	168	27	sub	sub	NOUN
ejpam-5300	168	28	-	-	NOUN
ejpam-5300	168	29	circles	circle	NOUN
ejpam-5300	168	30	.	.	PUNCT
ejpam-5300	169	1	when	when	SCONJ
ejpam-5300	169	2	generalized	generalize	VERB
ejpam-5300	169	3	to	to	ADP
ejpam-5300	169	4	n	n	PRON
ejpam-5300	169	5	sub	sub	NOUN
ejpam-5300	169	6	-	-	NOUN
ejpam-5300	169	7	circles	circle	NOUN
ejpam-5300	169	8	within	within	ADP
ejpam-5300	169	9	the	the	DET
ejpam-5300	169	10	same	same	ADJ
ejpam-5300	169	11	triangle	triangle	NOUN
ejpam-5300	169	12	,	,	PUNCT
ejpam-5300	169	13	separated	separate	VERB
ejpam-5300	169	14	by	by	ADP
ejpam-5300	169	15	cevians	cevian	NOUN
ejpam-5300	169	16	ab2	ab2	PROPN
ejpam-5300	169	17	,	,	PUNCT
ejpam-5300	169	18	the	the	DET
ejpam-5300	169	19	result	result	NOUN
ejpam-5300	169	20	revealed	reveal	VERB
ejpam-5300	169	21	that	that	SCONJ
ejpam-5300	169	22	the	the	DET
ejpam-5300	169	23	fraction	fraction	NOUN
ejpam-5300	169	24	between	between	ADP
ejpam-5300	169	25	any	any	DET
ejpam-5300	169	26	two	two	NUM
ejpam-5300	169	27	sub	sub	ADJ
ejpam-5300	169	28	-	-	ADJ
ejpam-5300	169	29	inscribed	inscribe	VERB
ejpam-5300	169	30	circles	circle	NOUN
ejpam-5300	169	31	radii	radii	VERB
ejpam-5300	169	32	forms	form	NOUN
ejpam-5300	169	33	a	a	DET
ejpam-5300	169	34	telescoping	telescope	VERB
ejpam-5300	169	35	product	product	NOUN
ejpam-5300	169	36	,	,	PUNCT
ejpam-5300	169	37	as	as	SCONJ
ejpam-5300	169	38	described	describe	VERB
ejpam-5300	169	39	in	in	ADP
ejpam-5300	169	40	section	section	NOUN
ejpam-5300	169	41	2	2	NUM
ejpam-5300	169	42	.	.	PUNCT
ejpam-5300	170	1	also	also	ADV
ejpam-5300	170	2	,	,	PUNCT
ejpam-5300	170	3	this	this	DET
ejpam-5300	170	4	paper	paper	NOUN
ejpam-5300	170	5	explores	explore	VERB
ejpam-5300	170	6	other	other	ADJ
ejpam-5300	170	7	generalized	generalized	ADJ
ejpam-5300	170	8	cases	case	NOUN
ejpam-5300	170	9	,	,	PUNCT
ejpam-5300	170	10	illustrating	illustrate	VERB
ejpam-5300	170	11	the	the	DET
ejpam-5300	170	12	relationship	relationship	NOUN
ejpam-5300	170	13	between	between	ADP
ejpam-5300	170	14	n	n	NOUN
ejpam-5300	170	15	sub	sub	ADJ
ejpam-5300	170	16	-	-	ADJ
ejpam-5300	170	17	inscribed	inscribe	VERB
ejpam-5300	170	18	circles	circle	NOUN
ejpam-5300	170	19	and	and	CCONJ
ejpam-5300	170	20	sub	sub	ADJ
ejpam-5300	170	21	-	-	ADJ
ejpam-5300	170	22	escribed	escribe	VERB
ejpam-5300	170	23	circles	circle	NOUN
ejpam-5300	170	24	,	,	PUNCT
ejpam-5300	170	25	as	as	SCONJ
ejpam-5300	170	26	shown	show	VERB
ejpam-5300	170	27	in	in	ADP
ejpam-5300	170	28	figure	figure	NOUN
ejpam-5300	170	29	9	9	NUM
ejpam-5300	170	30	.	.	PUNCT
ejpam-5300	171	1	our	our	PRON
ejpam-5300	171	2	findings	finding	NOUN
ejpam-5300	171	3	reveal	reveal	VERB
ejpam-5300	171	4	that	that	SCONJ
ejpam-5300	171	5	this	this	DET
ejpam-5300	171	6	formulation	formulation	NOUN
ejpam-5300	171	7	differs	differ	VERB
ejpam-5300	171	8	significantly	significantly	ADV
ejpam-5300	171	9	from	from	ADP
ejpam-5300	171	10	other	other	ADJ
ejpam-5300	171	11	sections	section	NOUN
ejpam-5300	171	12	,	,	PUNCT
ejpam-5300	171	13	as	as	SCONJ
ejpam-5300	171	14	the	the	DET
ejpam-5300	171	15	product	product	NOUN
ejpam-5300	171	16	of	of	ADP
ejpam-5300	171	17	their	their	PRON
ejpam-5300	171	18	relation	relation	NOUN
ejpam-5300	171	19	provides	provide	VERB
ejpam-5300	171	20	meaningful	meaningful	ADJ
ejpam-5300	171	21	interpretations	interpretation	NOUN
ejpam-5300	171	22	.	.	PUNCT
ejpam-5300	172	1	these	these	DET
ejpam-5300	172	2	relationships	relationship	NOUN
ejpam-5300	172	3	are	be	AUX
ejpam-5300	172	4	directly	directly	ADV
ejpam-5300	172	5	tied	tie	VERB
ejpam-5300	172	6	to	to	ADP
ejpam-5300	172	7	the	the	DET
ejpam-5300	172	8	radius	radius	NOUN
ejpam-5300	172	9	of	of	ADP
ejpam-5300	172	10	the	the	DET
ejpam-5300	172	11	largest	large	ADJ
ejpam-5300	172	12	circumcircle	circumcircle	NOUN
ejpam-5300	172	13	within	within	ADP
ejpam-5300	172	14	the	the	DET
ejpam-5300	172	15	same	same	ADJ
ejpam-5300	172	16	triangle	triangle	NOUN
ejpam-5300	172	17	.	.	PUNCT
ejpam-5300	173	1	references	reference	NOUN
ejpam-5300	173	2	4145	4145	NUM
ejpam-5300	173	3	on	on	ADP
ejpam-5300	173	4	the	the	DET
ejpam-5300	173	5	other	other	ADJ
ejpam-5300	173	6	hand	hand	NOUN
ejpam-5300	173	7	,	,	PUNCT
ejpam-5300	173	8	the	the	DET
ejpam-5300	173	9	study	study	NOUN
ejpam-5300	173	10	considers	consider	VERB
ejpam-5300	173	11	the	the	DET
ejpam-5300	173	12	scenario	scenario	NOUN
ejpam-5300	173	13	of	of	ADP
ejpam-5300	173	14	perpendicular	perpendicular	ADJ
ejpam-5300	173	15	triangles	triangle	NOUN
ejpam-5300	173	16	,	,	PUNCT
ejpam-5300	173	17	as	as	SCONJ
ejpam-5300	173	18	discussed	discuss	VERB
ejpam-5300	173	19	in	in	ADP
ejpam-5300	173	20	corollary	corollary	ADJ
ejpam-5300	173	21	1	1	NUM
ejpam-5300	173	22	,	,	PUNCT
ejpam-5300	173	23	presenting	present	VERB
ejpam-5300	173	24	the	the	DET
ejpam-5300	173	25	sum	sum	NOUN
ejpam-5300	173	26	of	of	ADP
ejpam-5300	173	27	the	the	DET
ejpam-5300	173	28	radii	radius	NOUN
ejpam-5300	173	29	of	of	ADP
ejpam-5300	173	30	all	all	DET
ejpam-5300	173	31	circles	circle	NOUN
ejpam-5300	173	32	in	in	ADP
ejpam-5300	173	33	these	these	DET
ejpam-5300	173	34	configurations	configuration	NOUN
ejpam-5300	173	35	.	.	PUNCT
ejpam-5300	174	1	this	this	DET
ejpam-5300	174	2	case	case	NOUN
ejpam-5300	174	3	guides	guide	VERB
ejpam-5300	174	4	us	we	PRON
ejpam-5300	174	5	toward	toward	ADP
ejpam-5300	174	6	understanding	understand	VERB
ejpam-5300	174	7	the	the	DET
ejpam-5300	174	8	perpendicular	perpendicular	ADJ
ejpam-5300	174	9	scenario	scenario	NOUN
ejpam-5300	174	10	.	.	PUNCT
ejpam-5300	175	1	at	at	ADP
ejpam-5300	175	2	the	the	DET
ejpam-5300	175	3	same	same	ADJ
ejpam-5300	175	4	time	time	NOUN
ejpam-5300	175	5	,	,	PUNCT
ejpam-5300	175	6	our	our	PRON
ejpam-5300	175	7	findings	finding	NOUN
ejpam-5300	175	8	also	also	ADV
ejpam-5300	175	9	consider	consider	VERB
ejpam-5300	175	10	the	the	DET
ejpam-5300	175	11	angle	angle	NOUN
ejpam-5300	175	12	-	-	PUNCT
ejpam-5300	175	13	bisector	bisector	NOUN
ejpam-5300	175	14	case	case	NOUN
ejpam-5300	175	15	,	,	PUNCT
ejpam-5300	175	16	a	a	DET
ejpam-5300	175	17	general	general	ADJ
ejpam-5300	175	18	concept	concept	NOUN
ejpam-5300	175	19	frequently	frequently	ADV
ejpam-5300	175	20	encountered	encounter	VERB
ejpam-5300	175	21	in	in	ADP
ejpam-5300	175	22	problem	problem	NOUN
ejpam-5300	175	23	-	-	PUNCT
ejpam-5300	175	24	solving	solving	NOUN
ejpam-5300	175	25	across	across	ADP
ejpam-5300	175	26	many	many	ADJ
ejpam-5300	175	27	sources	source	NOUN
ejpam-5300	175	28	.	.	PUNCT
ejpam-5300	176	1	this	this	DET
ejpam-5300	176	2	finding	finding	NOUN
ejpam-5300	176	3	demonstrates	demonstrate	VERB
ejpam-5300	176	4	a	a	DET
ejpam-5300	176	5	novel	novel	ADJ
ejpam-5300	176	6	approach	approach	NOUN
ejpam-5300	176	7	with	with	ADP
ejpam-5300	176	8	applications	application	NOUN
ejpam-5300	176	9	in	in	ADP
ejpam-5300	176	10	many	many	ADJ
ejpam-5300	176	11	fields	field	NOUN
ejpam-5300	176	12	,	,	PUNCT
ejpam-5300	176	13	such	such	ADJ
ejpam-5300	176	14	as	as	ADP
ejpam-5300	176	15	mathematical	mathematical	ADJ
ejpam-5300	176	16	education	education	NOUN
ejpam-5300	176	17	,	,	PUNCT
ejpam-5300	176	18	particularly	particularly	ADV
ejpam-5300	176	19	through	through	ADP
ejpam-5300	176	20	the	the	DET
ejpam-5300	176	21	development	development	NOUN
ejpam-5300	176	22	of	of	ADP
ejpam-5300	176	23	new	new	ADJ
ejpam-5300	176	24	geometry	geometry	NOUN
ejpam-5300	176	25	teaching	teaching	NOUN
ejpam-5300	176	26	materials	material	NOUN
ejpam-5300	176	27	[	[	X
ejpam-5300	176	28	see	see	VERB
ejpam-5300	176	29	also	also	ADV
ejpam-5300	176	30	[	[	X
ejpam-5300	176	31	9	9	NUM
ejpam-5300	176	32	]	]	SYM
ejpam-5300	176	33	]	]	PUNCT
ejpam-5300	176	34	as	as	ADP
ejpam-5300	176	35	a	a	DET
ejpam-5300	176	36	technical	technical	ADJ
ejpam-5300	176	37	report	report	NOUN
ejpam-5300	176	38	.	.	PUNCT
ejpam-5300	177	1	additionally	additionally	ADV
ejpam-5300	177	2	,	,	PUNCT
ejpam-5300	177	3	it	it	PRON
ejpam-5300	177	4	offers	offer	VERB
ejpam-5300	177	5	potential	potential	NOUN
ejpam-5300	177	6	for	for	ADP
ejpam-5300	177	7	the	the	DET
ejpam-5300	177	8	progression	progression	NOUN
ejpam-5300	177	9	of	of	ADP
ejpam-5300	177	10	optimization	optimization	NOUN
ejpam-5300	177	11	methods	method	NOUN
ejpam-5300	177	12	[	[	X
ejpam-5300	177	13	[	[	X
ejpam-5300	177	14	8	8	NUM
ejpam-5300	177	15	]	]	X
ejpam-5300	177	16	]	]	X
ejpam-5300	177	17	is	be	AUX
ejpam-5300	177	18	a	a	DET
ejpam-5300	177	19	journal	journal	ADJ
ejpam-5300	177	20	article	article	NOUN
ejpam-5300	177	21	and	and	CCONJ
ejpam-5300	177	22	research	research	NOUN
ejpam-5300	177	23	in	in	ADP
ejpam-5300	177	24	mathematical	mathematical	ADJ
ejpam-5300	177	25	history	history	NOUN
ejpam-5300	177	26	.	.	PUNCT
ejpam-5300	178	1	acknowledgements	acknowledgement	NOUN
ejpam-5300	178	2	the	the	DET
ejpam-5300	178	3	author	author	NOUN
ejpam-5300	178	4	conveys	convey	VERB
ejpam-5300	178	5	sincere	sincere	ADJ
ejpam-5300	178	6	appreciation	appreciation	NOUN
ejpam-5300	178	7	to	to	ADP
ejpam-5300	178	8	mrs	mrs	PROPN
ejpam-5300	178	9	.	.	PROPN
ejpam-5300	178	10	ratree	ratree	PROPN
ejpam-5300	178	11	boonsomchua	boonsomchua	PROPN
ejpam-5300	178	12	,	,	PUNCT
ejpam-5300	178	13	an	an	DET
ejpam-5300	178	14	accomplished	accomplished	ADJ
ejpam-5300	178	15	mathematics	mathematics	NOUN
ejpam-5300	178	16	teacher	teacher	NOUN
ejpam-5300	178	17	and	and	CCONJ
ejpam-5300	178	18	advisor	advisor	NOUN
ejpam-5300	178	19	at	at	ADP
ejpam-5300	178	20	surasakmontri	surasakmontri	PROPN
ejpam-5300	178	21	school	school	NOUN
ejpam-5300	178	22	,	,	PUNCT
ejpam-5300	178	23	whose	whose	DET
ejpam-5300	178	24	guidance	guidance	NOUN
ejpam-5300	178	25	was	be	AUX
ejpam-5300	178	26	instrumental	instrumental	ADJ
ejpam-5300	178	27	in	in	ADP
ejpam-5300	178	28	preparing	prepare	VERB
ejpam-5300	178	29	this	this	DET
ejpam-5300	178	30	paper	paper	NOUN
ejpam-5300	178	31	.	.	PUNCT
ejpam-5300	179	1	her	her	PRON
ejpam-5300	179	2	notable	notable	ADJ
ejpam-5300	179	3	achievements	achievement	NOUN
ejpam-5300	179	4	include	include	VERB
ejpam-5300	179	5	a	a	DET
ejpam-5300	179	6	gold	gold	NOUN
ejpam-5300	179	7	award	award	NOUN
ejpam-5300	179	8	at	at	ADP
ejpam-5300	179	9	the	the	DET
ejpam-5300	179	10	2nd	2nd	ADJ
ejpam-5300	179	11	international	international	ADJ
ejpam-5300	179	12	conference	conference	NOUN
ejpam-5300	179	13	for	for	ADP
ejpam-5300	179	14	students	student	NOUN
ejpam-5300	179	15	in	in	ADP
ejpam-5300	179	16	science	science	NOUN
ejpam-5300	179	17	and	and	CCONJ
ejpam-5300	179	18	innovation	innovation	NOUN
ejpam-5300	179	19	2022	2022	NUM
ejpam-5300	179	20	(	(	PUNCT
ejpam-5300	179	21	issi	issi	PROPN
ejpam-5300	179	22	2nd	2nd	PROPN
ejpam-5300	179	23	)	)	PUNCT
ejpam-5300	179	24	,	,	PUNCT
ejpam-5300	179	25	organized	organize	VERB
ejpam-5300	179	26	by	by	ADP
ejpam-5300	179	27	the	the	DET
ejpam-5300	179	28	institute	institute	NOUN
ejpam-5300	179	29	for	for	ADP
ejpam-5300	179	30	the	the	DET
ejpam-5300	179	31	promotion	promotion	NOUN
ejpam-5300	179	32	of	of	ADP
ejpam-5300	179	33	teaching	teach	VERB
ejpam-5300	179	34	science	science	NOUN
ejpam-5300	179	35	and	and	CCONJ
ejpam-5300	179	36	technology	technology	NOUN
ejpam-5300	179	37	(	(	PUNCT
ejpam-5300	179	38	ipst	ipst	ADJ
ejpam-5300	179	39	)	)	PUNCT
ejpam-5300	179	40	.	.	PUNCT
ejpam-5300	180	1	further	far	ADV
ejpam-5300	180	2	thanks	thank	NOUN
ejpam-5300	180	3	to	to	ADP
ejpam-5300	180	4	mrs	mrs	PROPN
ejpam-5300	180	5	.	.	PROPN
ejpam-5300	180	6	chalida	chalida	PROPN
ejpam-5300	180	7	suwankosai	suwankosai	PROPN
ejpam-5300	180	8	,	,	PUNCT
ejpam-5300	180	9	a	a	DET
ejpam-5300	180	10	mathematics	mathematics	NOUN
ejpam-5300	180	11	teacher	teacher	NOUN
ejpam-5300	180	12	at	at	ADP
ejpam-5300	180	13	benjamarachanusorn	benjamarachanusorn	VERB
ejpam-5300	180	14	school	school	NOUN
ejpam-5300	180	15	,	,	PUNCT
ejpam-5300	180	16	for	for	ADP
ejpam-5300	180	17	her	her	PRON
ejpam-5300	180	18	insightful	insightful	ADJ
ejpam-5300	180	19	recommendations	recommendation	NOUN
ejpam-5300	180	20	that	that	PRON
ejpam-5300	180	21	have	have	AUX
ejpam-5300	180	22	greatly	greatly	ADV
ejpam-5300	180	23	expanded	expand	VERB
ejpam-5300	180	24	the	the	DET
ejpam-5300	180	25	study	study	NOUN
ejpam-5300	180	26	’s	’s	PART
ejpam-5300	180	27	scope	scope	NOUN
ejpam-5300	180	28	,	,	PUNCT
ejpam-5300	180	29	with	with	ADP
ejpam-5300	180	30	influences	influence	NOUN
ejpam-5300	180	31	dating	date	VERB
ejpam-5300	180	32	back	back	ADV
ejpam-5300	180	33	to	to	ADP
ejpam-5300	180	34	the	the	DET
ejpam-5300	180	35	author	author	NOUN
ejpam-5300	180	36	’s	’s	PART
ejpam-5300	180	37	ninth	ninth	ADJ
ejpam-5300	180	38	-	-	PUNCT
ejpam-5300	180	39	grade	grade	NOUN
ejpam-5300	180	40	year	year	NOUN
ejpam-5300	180	41	.	.	PUNCT
ejpam-5300	181	1	profound	profound	ADJ
ejpam-5300	181	2	gratitude	gratitude	NOUN
ejpam-5300	181	3	is	be	AUX
ejpam-5300	181	4	also	also	ADV
ejpam-5300	181	5	extended	extend	VERB
ejpam-5300	181	6	to	to	ADP
ejpam-5300	181	7	mr	mr	PROPN
ejpam-5300	181	8	.	.	PROPN
ejpam-5300	181	9	taechasith	taechasith	PROPN
ejpam-5300	181	10	kangkhuntod	kangkhuntod	PROPN
ejpam-5300	181	11	,	,	PUNCT
ejpam-5300	181	12	studying	study	VERB
ejpam-5300	181	13	at	at	ADP
ejpam-5300	181	14	rajsimawittayalai	rajsimawittayalai	PROPN
ejpam-5300	181	15	school	school	PROPN
ejpam-5300	181	16	,	,	PUNCT
ejpam-5300	181	17	and	and	CCONJ
ejpam-5300	181	18	former	former	ADJ
ejpam-5300	181	19	chief	chief	ADJ
ejpam-5300	181	20	executive	executive	ADJ
ejpam-5300	181	21	officer	officer	NOUN
ejpam-5300	181	22	at	at	ADP
ejpam-5300	181	23	creativelab	creativelab	PROPN
ejpam-5300	181	24	,	,	PUNCT
ejpam-5300	181	25	an	an	DET
ejpam-5300	181	26	independent	independent	ADJ
ejpam-5300	181	27	organization	organization	NOUN
ejpam-5300	181	28	.	.	PUNCT
ejpam-5300	182	1	he	he	PRON
ejpam-5300	182	2	organized	organize	VERB
ejpam-5300	182	3	a	a	DET
ejpam-5300	182	4	crucial	crucial	ADJ
ejpam-5300	182	5	meeting	meeting	NOUN
ejpam-5300	182	6	on	on	ADP
ejpam-5300	182	7	april	april	PROPN
ejpam-5300	182	8	21	21	NUM
ejpam-5300	182	9	,	,	PUNCT
ejpam-5300	182	10	2024	2024	NUM
ejpam-5300	182	11	,	,	PUNCT
ejpam-5300	182	12	covering	cover	VERB
ejpam-5300	182	13	diverse	diverse	ADJ
ejpam-5300	182	14	fields	field	NOUN
ejpam-5300	182	15	like	like	ADP
ejpam-5300	182	16	mathematics	mathematic	NOUN
ejpam-5300	182	17	,	,	PUNCT
ejpam-5300	182	18	physics	physics	NOUN
ejpam-5300	182	19	,	,	PUNCT
ejpam-5300	182	20	architecture	architecture	NOUN
ejpam-5300	182	21	,	,	PUNCT
ejpam-5300	182	22	and	and	CCONJ
ejpam-5300	182	23	history	history	NOUN
ejpam-5300	182	24	.	.	PUNCT
ejpam-5300	183	1	this	this	DET
ejpam-5300	183	2	meeting	meeting	NOUN
ejpam-5300	183	3	significantly	significantly	ADV
ejpam-5300	183	4	inspired	inspire	VERB
ejpam-5300	183	5	the	the	DET
ejpam-5300	183	6	integration	integration	NOUN
ejpam-5300	183	7	of	of	ADP
ejpam-5300	183	8	modern	modern	ADJ
ejpam-5300	183	9	mathematical	mathematical	ADJ
ejpam-5300	183	10	methods	method	NOUN
ejpam-5300	183	11	with	with	ADP
ejpam-5300	183	12	traditional	traditional	ADJ
ejpam-5300	183	13	sangaku	sangaku	NOUN
ejpam-5300	183	14	problems	problem	NOUN
ejpam-5300	183	15	.	.	PUNCT
ejpam-5300	184	1	references	reference	NOUN
ejpam-5300	184	2	[	[	X
ejpam-5300	184	3	1	1	NUM
ejpam-5300	184	4	]	]	SYM
ejpam-5300	184	5	2018	2018	NUM
ejpam-5300	184	6	aime	aime	NOUN
ejpam-5300	184	7	i	i	PRON
ejpam-5300	184	8	problems	problem	NOUN
ejpam-5300	184	9	,	,	PUNCT
ejpam-5300	184	10	problem	problem	NOUN
ejpam-5300	184	11	13	13	NUM
ejpam-5300	184	12	.	.	PUNCT
ejpam-5300	185	1	american	american	ADJ
ejpam-5300	185	2	mathematics	mathematics	PROPN
ejpam-5300	185	3	competitions	competition	NOUN
ejpam-5300	185	4	(	(	PUNCT
ejpam-5300	185	5	amc	amc	PROPN
ejpam-5300	185	6	)	)	PUNCT
ejpam-5300	185	7	,	,	PUNCT
ejpam-5300	185	8	mathematical	mathematical	ADJ
ejpam-5300	185	9	association	association	PROPN
ejpam-5300	185	10	of	of	ADP
ejpam-5300	185	11	america	america	PROPN
ejpam-5300	185	12	,	,	PUNCT
ejpam-5300	185	13	2018	2018	NUM
ejpam-5300	185	14	.	.	PUNCT
ejpam-5300	186	1	[	[	X
ejpam-5300	186	2	2	2	X
ejpam-5300	186	3	]	]	PUNCT
ejpam-5300	186	4	e.	e.	PROPN
ejpam-5300	186	5	a.	a.	PROPN
ejpam-5300	186	6	donovan	donovan	PROPN
ejpam-5300	186	7	,	,	PUNCT
ejpam-5300	186	8	a.	a.	NOUN
ejpam-5300	186	9	hoots	hoot	NOUN
ejpam-5300	186	10	,	,	PUNCT
ejpam-5300	186	11	and	and	CCONJ
ejpam-5300	186	12	l.	l.	PROPN
ejpam-5300	186	13	w.	w.	PROPN
ejpam-5300	186	14	wiglesworth	wiglesworth	PROPN
ejpam-5300	186	15	.	.	PUNCT
ejpam-5300	187	1	japanese	japanese	ADJ
ejpam-5300	187	2	temple	temple	PROPN
ejpam-5300	187	3	geometry	geometry	NOUN
ejpam-5300	187	4	.	.	PUNCT
ejpam-5300	188	1	teaching	teach	VERB
ejpam-5300	188	2	mathematics	mathematic	NOUN
ejpam-5300	188	3	through	through	ADP
ejpam-5300	188	4	cross	cross	ADJ
ejpam-5300	188	5	-	-	ADJ
ejpam-5300	188	6	curricular	curricular	ADJ
ejpam-5300	188	7	projects	project	NOUN
ejpam-5300	188	8	,	,	PUNCT
ejpam-5300	188	9	72:51–62	72:51–62	NOUN
ejpam-5300	188	10	,	,	PUNCT
ejpam-5300	188	11	2024	2024	NUM
ejpam-5300	188	12	.	.	PUNCT
ejpam-5300	189	1	[	[	X
ejpam-5300	189	2	3	3	X
ejpam-5300	189	3	]	]	PUNCT
ejpam-5300	189	4	a.	a.	NOUN
ejpam-5300	189	5	drei	drei	PROPN
ejpam-5300	189	6	.	.	PUNCT
ejpam-5300	190	1	equal	equal	ADJ
ejpam-5300	190	2	incircles	incircle	NOUN
ejpam-5300	190	3	theorem	theorem	PROPN
ejpam-5300	190	4	,	,	PUNCT
ejpam-5300	190	5	angela	angela	PROPN
ejpam-5300	190	6	drei	drei	PROPN
ejpam-5300	190	7	’s	’s	PART
ejpam-5300	190	8	proof	proof	NOUN
ejpam-5300	190	9	.	.	PUNCT
ejpam-5300	191	1	cut	cut	VERB
ejpam-5300	191	2	-	-	PUNCT
ejpam-5300	191	3	the	the	DET
ejpam-5300	191	4	-	-	PUNCT
ejpam-5300	191	5	knot	knot	NOUN
ejpam-5300	191	6	,	,	PUNCT
ejpam-5300	191	7	2011	2011	NUM
ejpam-5300	191	8	.	.	PUNCT
ejpam-5300	192	1	[	[	X
ejpam-5300	192	2	4	4	X
ejpam-5300	192	3	]	]	PUNCT
ejpam-5300	192	4	r.	r.	PROPN
ejpam-5300	192	5	y.	y.	PROPN
ejpam-5300	192	6	a.	a.	PROPN
ejpam-5300	192	7	n.	n.	PROPN
ejpam-5300	192	8	fameli	fameli	PROPN
ejpam-5300	192	9	.	.	PUNCT
ejpam-5300	193	1	math	math	PROPN
ejpam-5300	193	2	400	400	NUM
ejpam-5300	193	3	:	:	PUNCT
ejpam-5300	193	4	sangaku	sangaku	PROPN
ejpam-5300	193	5	,	,	PUNCT
ejpam-5300	193	6	japanese	japanese	ADJ
ejpam-5300	193	7	temple	temple	PROPN
ejpam-5300	193	8	geometry	geometry	NOUN
ejpam-5300	193	9	.	.	PUNCT
ejpam-5300	194	1	https://	https://	PROPN
ejpam-5300	194	2	cklixx.people.wm.edu/teaching/math400/fameli.pdf	cklixx.people.wm.edu/teaching/math400/fameli.pdf	NOUN
ejpam-5300	194	3	,	,	PUNCT
ejpam-5300	194	4	2020	2020	NUM
ejpam-5300	194	5	.	.	PUNCT
ejpam-5300	195	1	accessed	access	VERB
ejpam-5300	195	2	:	:	PUNCT
ejpam-5300	195	3	2	2	NUM
ejpam-5300	195	4	,	,	PUNCT
ejpam-5300	195	5	2023	2023	NUM
ejpam-5300	195	6	.	.	PUNCT
ejpam-5300	196	1	[	[	X
ejpam-5300	196	2	5	5	X
ejpam-5300	196	3	]	]	PUNCT
ejpam-5300	196	4	h.	h.	PROPN
ejpam-5300	196	5	fukagawa	fukagawa	PROPN
ejpam-5300	196	6	and	and	CCONJ
ejpam-5300	196	7	t.	t.	PROPN
ejpam-5300	196	8	rothman	rothman	PROPN
ejpam-5300	196	9	.	.	PUNCT
ejpam-5300	197	1	japanese	japanese	ADJ
ejpam-5300	197	2	temple	temple	PROPN
ejpam-5300	197	3	geometry	geometry	NOUN
ejpam-5300	197	4	problems	problem	NOUN
ejpam-5300	197	5	.	.	PUNCT
ejpam-5300	198	1	scientific	scientific	ADJ
ejpam-5300	198	2	american	american	PROPN
ejpam-5300	198	3	,	,	PUNCT
ejpam-5300	198	4	278(5):84–91	278(5):84–91	NUM
ejpam-5300	198	5	,	,	PUNCT
ejpam-5300	198	6	1989	1989	NUM
ejpam-5300	198	7	.	.	PUNCT
ejpam-5300	199	1	[	[	X
ejpam-5300	199	2	6	6	NUM
ejpam-5300	199	3	]	]	X
ejpam-5300	199	4	n.	n.	PROPN
ejpam-5300	199	5	hartmann	hartmann	PROPN
ejpam-5300	199	6	.	.	PROPN
ejpam-5300	200	1	sangaku	sangaku	PROPN
ejpam-5300	200	2	in	in	ADP
ejpam-5300	200	3	multiple	multiple	ADJ
ejpam-5300	200	4	geometries	geometry	NOUN
ejpam-5300	200	5	:	:	PUNCT
ejpam-5300	200	6	examining	examine	VERB
ejpam-5300	200	7	japanese	japanese	ADJ
ejpam-5300	200	8	temple	temple	PROPN
ejpam-5300	200	9	geometry	geometry	NOUN
ejpam-5300	200	10	beyond	beyond	ADP
ejpam-5300	200	11	euclid	euclid	PROPN
ejpam-5300	200	12	,	,	PUNCT
ejpam-5300	200	13	2022	2022	NUM
ejpam-5300	200	14	.	.	PUNCT
ejpam-5300	201	1	[	[	X
ejpam-5300	201	2	7	7	X
ejpam-5300	201	3	]	]	X
ejpam-5300	201	4	r.	r.	PROPN
ejpam-5300	201	5	hosking	hosking	PROPN
ejpam-5300	201	6	.	.	PUNCT
ejpam-5300	202	1	solving	solve	VERB
ejpam-5300	202	2	sangaku	sangaku	NOUN
ejpam-5300	202	3	:	:	PUNCT
ejpam-5300	202	4	a	a	DET
ejpam-5300	202	5	traditional	traditional	ADJ
ejpam-5300	202	6	solution	solution	NOUN
ejpam-5300	202	7	to	to	ADP
ejpam-5300	202	8	a	a	DET
ejpam-5300	202	9	nineteenth	nineteenth	ADJ
ejpam-5300	202	10	-	-	PUNCT
ejpam-5300	202	11	century	century	NOUN
ejpam-5300	202	12	japanese	japanese	ADJ
ejpam-5300	202	13	temple	temple	PROPN
ejpam-5300	202	14	problem	problem	NOUN
ejpam-5300	202	15	.	.	PUNCT
ejpam-5300	203	1	journal	journal	PROPN
ejpam-5300	203	2	for	for	ADP
ejpam-5300	203	3	history	history	NOUN
ejpam-5300	203	4	of	of	ADP
ejpam-5300	203	5	mathematics	mathematic	NOUN
ejpam-5300	203	6	,	,	PUNCT
ejpam-5300	203	7	30:53–62	30:53–62	NUM
ejpam-5300	203	8	,	,	PUNCT
ejpam-5300	203	9	2017	2017	NUM
ejpam-5300	203	10	.	.	PUNCT
ejpam-5300	204	1	[	[	X
ejpam-5300	204	2	8	8	NUM
ejpam-5300	204	3	]	]	X
ejpam-5300	204	4	d.	d.	PROPN
ejpam-5300	204	5	jargalsaikhan	jargalsaikhan	PROPN
ejpam-5300	204	6	,	,	PUNCT
ejpam-5300	204	7	d.	d.	PROPN
ejpam-5300	204	8	rentsen	rentsen	PROPN
ejpam-5300	204	9	,	,	PUNCT
ejpam-5300	204	10	and	and	CCONJ
ejpam-5300	204	11	b.	b.	PROPN
ejpam-5300	204	12	darkhijav	darkhijav	PROPN
ejpam-5300	204	13	.	.	PUNCT
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ejpam-5300	205	2	on	on	ADP
ejpam-5300	205	3	sangaku	sangaku	PROPN
ejpam-5300	205	4	problem	problem	NOUN
ejpam-5300	205	5	using	use	VERB
ejpam-5300	205	6	optimization	optimization	NOUN
ejpam-5300	205	7	methods	method	NOUN
ejpam-5300	205	8	.	.	PUNCT
ejpam-5300	206	1	journal	journal	PROPN
ejpam-5300	206	2	of	of	ADP
ejpam-5300	206	3	institute	institute	PROPN
ejpam-5300	206	4	of	of	ADP
ejpam-5300	206	5	mathematics	mathematics	PROPN
ejpam-5300	206	6	and	and	CCONJ
ejpam-5300	206	7	digital	digital	ADJ
ejpam-5300	206	8	technology	technology	NOUN
ejpam-5300	206	9	,	,	PUNCT
ejpam-5300	206	10	5(1):19–29	5(1):19–29	NUM
ejpam-5300	206	11	,	,	PUNCT
ejpam-5300	206	12	2023	2023	NUM
ejpam-5300	206	13	.	.	PUNCT
ejpam-5300	207	1	https://cklixx.people.wm.edu/teaching/math400/fameli.pdf	https://cklixx.people.wm.edu/teaching/math400/fameli.pdf	PROPN
ejpam-5300	207	2	https://cklixx.people.wm.edu/teaching/math400/fameli.pdf	https://cklixx.people.wm.edu/teaching/math400/fameli.pdf	PROPN
ejpam-5300	207	3	references	reference	NOUN
ejpam-5300	207	4	4146	4146	NUM
ejpam-5300	208	1	[	[	X
ejpam-5300	208	2	9	9	NUM
ejpam-5300	208	3	]	]	X
ejpam-5300	208	4	h.	h.	PROPN
ejpam-5300	208	5	makishita	makishita	PROPN
ejpam-5300	208	6	.	.	PUNCT
ejpam-5300	209	1	solving	solve	VERB
ejpam-5300	209	2	problems	problem	NOUN
ejpam-5300	209	3	from	from	ADP
ejpam-5300	209	4	sangaku	sangaku	NOUN
ejpam-5300	209	5	with	with	ADP
ejpam-5300	209	6	technology	technology	NOUN
ejpam-5300	209	7	—	—	PUNCT
ejpam-5300	209	8	for	for	ADP
ejpam-5300	209	9	good	good	ADJ
ejpam-5300	209	10	mathematics	mathematic	NOUN
ejpam-5300	209	11	in	in	ADP
ejpam-5300	209	12	education	education	NOUN
ejpam-5300	209	13	,	,	PUNCT
ejpam-5300	209	14	2010	2010	NUM
ejpam-5300	209	15	.	.	PUNCT
ejpam-5300	210	1	[	[	X
ejpam-5300	210	2	10	10	NUM
ejpam-5300	210	3	]	]	X
ejpam-5300	210	4	m.	m.	NOUN
ejpam-5300	210	5	tibi	tibi	PROPN
ejpam-5300	210	6	,	,	PUNCT
ejpam-5300	210	7	g.	g.	PROPN
ejpam-5300	210	8	zanardo	zanardo	PROPN
ejpam-5300	210	9	,	,	PUNCT
ejpam-5300	210	10	e.	e.	PROPN
ejpam-5300	210	11	vendraminett	vendraminett	PROPN
ejpam-5300	210	12	,	,	PUNCT
ejpam-5300	210	13	d.	d.	PROPN
ejpam-5300	210	14	pozzebon	pozzebon	PROPN
ejpam-5300	210	15	,	,	PUNCT
ejpam-5300	210	16	l.	l.	PROPN
ejpam-5300	210	17	zaccaron	zaccaron	PROPN
ejpam-5300	210	18	,	,	PUNCT
ejpam-5300	210	19	m.	m.	NOUN
ejpam-5300	210	20	breda	breda	PROPN
ejpam-5300	210	21	,	,	PUNCT
ejpam-5300	210	22	i.	i.	NOUN
ejpam-5300	210	23	emeliyanov	emeliyanov	PROPN
ejpam-5300	210	24	,	,	PUNCT
ejpam-5300	210	25	and	and	CCONJ
ejpam-5300	210	26	l.	l.	PROPN
ejpam-5300	210	27	bonaldo	bonaldo	PROPN
ejpam-5300	210	28	.	.	PUNCT
ejpam-5300	211	1	two	two	NUM
ejpam-5300	211	2	problems	problem	NOUN
ejpam-5300	211	3	on	on	ADP
ejpam-5300	211	4	touching	touching	ADJ
ejpam-5300	211	5	circles	circle	NOUN
ejpam-5300	211	6	and	and	CCONJ
ejpam-5300	211	7	their	their	PRON
ejpam-5300	211	8	connection	connection	NOUN
ejpam-5300	211	9	to	to	ADP
ejpam-5300	211	10	the	the	DET
ejpam-5300	211	11	stern	stern	ADJ
ejpam-5300	211	12	-	-	PUNCT
ejpam-5300	211	13	brocot	brocot	NOUN
ejpam-5300	211	14	tree	tree	NOUN
ejpam-5300	211	15	.	.	PUNCT
ejpam-5300	212	1	school	school	NOUN
ejpam-5300	212	2	:	:	PUNCT
ejpam-5300	212	3	liceo	liceo	PROPN
ejpam-5300	212	4	“	"	PUNCT
ejpam-5300	212	5	m.	m.	NOUN
ejpam-5300	212	6	casagrande	casagrande	PROPN
ejpam-5300	212	7	”	"	PUNCT
ejpam-5300	212	8	–	–	PUNCT
ejpam-5300	212	9	pieve	pieve	PROPN
ejpam-5300	212	10	di	di	X
ejpam-5300	212	11	soligo	soligo	PROPN
ejpam-5300	212	12	,	,	PUNCT
ejpam-5300	212	13	treviso	treviso	PROPN
ejpam-5300	212	14	(	(	PUNCT
ejpam-5300	212	15	italy	italy	PROPN
ejpam-5300	212	16	)	)	PUNCT
ejpam-5300	212	17	,	,	PUNCT
ejpam-5300	212	18	2021	2021	NUM
ejpam-5300	212	19	.	.	PUNCT
ejpam-5300	213	1	introduction	introduction	NOUN
ejpam-5300	213	2	main	main	ADJ
ejpam-5300	213	3	results	result	NOUN
ejpam-5300	213	4	discussions	discussion	NOUN
ejpam-5300	213	5	and	and	CCONJ
ejpam-5300	213	6	conclusions	conclusion	NOUN