id	sid	tid	token	lemma	pos
ejpam-3605	1	1	european	european	PROPN
ejpam-3605	1	2	journal	journal	PROPN
ejpam-3605	1	3	of	of	ADP
ejpam-3605	1	4	pure	pure	ADJ
ejpam-3605	1	5	and	and	CCONJ
ejpam-3605	1	6	applied	apply	VERB
ejpam-3605	1	7	mathematics	mathematic	NOUN
ejpam-3605	1	8	vol	vol	NOUN
ejpam-3605	1	9	.	.	PROPN
ejpam-3605	2	1	13	13	NUM
ejpam-3605	2	2	,	,	PUNCT
ejpam-3605	2	3	no	no	INTJ
ejpam-3605	2	4	.	.	NOUN
ejpam-3605	2	5	1	1	NUM
ejpam-3605	2	6	,	,	PUNCT
ejpam-3605	2	7	2020	2020	NUM
ejpam-3605	2	8	,	,	PUNCT
ejpam-3605	2	9	180	180	NUM
ejpam-3605	2	10	-	-	SYM
ejpam-3605	2	11	184	184	NUM
ejpam-3605	2	12	issn	issn	PROPN
ejpam-3605	2	13	1307	1307	NUM
ejpam-3605	2	14	-	-	SYM
ejpam-3605	2	15	5543	5543	NUM
ejpam-3605	2	16	–	–	PUNCT
ejpam-3605	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3605	2	18	published	publish	VERB
ejpam-3605	2	19	by	by	ADP
ejpam-3605	2	20	new	new	PROPN
ejpam-3605	2	21	york	york	PROPN
ejpam-3605	2	22	business	business	PROPN
ejpam-3605	2	23	global	global	VERB
ejpam-3605	2	24	some	some	DET
ejpam-3605	2	25	applications	application	NOUN
ejpam-3605	2	26	of	of	ADP
ejpam-3605	2	27	ptolemy	ptolemy	PROPN
ejpam-3605	2	28	’s	’s	PART
ejpam-3605	2	29	theorem	theorem	NOUN
ejpam-3605	2	30	in	in	ADP
ejpam-3605	2	31	secondary	secondary	ADJ
ejpam-3605	2	32	school	school	NOUN
ejpam-3605	2	33	mathematics	mathematic	NOUN
ejpam-3605	2	34	samed	same	VERB
ejpam-3605	2	35	j.aliyev1,∗	j.aliyev1,∗	NOUN
ejpam-3605	2	36	,	,	PUNCT
ejpam-3605	2	37	shalala	shalala	PROPN
ejpam-3605	2	38	a.hamidova1	a.hamidova1	PROPN
ejpam-3605	2	39	,	,	PUNCT
ejpam-3605	2	40	goncha	goncha	PROPN
ejpam-3605	2	41	z.abdullayeva1	z.abdullayeva1	PROPN
ejpam-3605	2	42	1	1	NUM
ejpam-3605	2	43	department	department	NOUN
ejpam-3605	2	44	of	of	ADP
ejpam-3605	2	45	methods	method	NOUN
ejpam-3605	2	46	of	of	ADP
ejpam-3605	2	47	mathematics	mathematic	NOUN
ejpam-3605	2	48	and	and	CCONJ
ejpam-3605	2	49	its	its	PRON
ejpam-3605	2	50	teaching	teaching	NOUN
ejpam-3605	2	51	,	,	PUNCT
ejpam-3605	2	52	faculty	faculty	NOUN
ejpam-3605	2	53	of	of	ADP
ejpam-3605	2	54	mechanics	mechanic	NOUN
ejpam-3605	2	55	and	and	CCONJ
ejpam-3605	2	56	mathematics	mathematic	NOUN
ejpam-3605	2	57	,	,	PUNCT
ejpam-3605	2	58	baku	baku	PROPN
ejpam-3605	2	59	state	state	PROPN
ejpam-3605	2	60	university	university	PROPN
ejpam-3605	2	61	,	,	PUNCT
ejpam-3605	2	62	baku	baku	PROPN
ejpam-3605	2	63	,	,	PUNCT
ejpam-3605	2	64	z.khalilov	z.khalilov	PROPN
ejpam-3605	2	65	str.23	str.23	NOUN
ejpam-3605	2	66	,	,	PUNCT
ejpam-3605	2	67	,	,	PUNCT
ejpam-3605	2	68	az1148	az1148	PROPN
ejpam-3605	2	69	,	,	PUNCT
ejpam-3605	2	70	azerbaijan	azerbaijan	PROPN
ejpam-3605	2	71	abstract	abstract	NOUN
ejpam-3605	2	72	.	.	PUNCT
ejpam-3605	3	1	we	we	PRON
ejpam-3605	3	2	consider	consider	VERB
ejpam-3605	3	3	some	some	DET
ejpam-3605	3	4	applications	application	NOUN
ejpam-3605	3	5	of	of	ADP
ejpam-3605	3	6	ptolemy	ptolemy	PROPN
ejpam-3605	3	7	’s	’s	PART
ejpam-3605	3	8	theorem	theorem	PROPN
ejpam-3605	3	9	.	.	PUNCT
ejpam-3605	4	1	in	in	ADP
ejpam-3605	4	2	particular	particular	ADJ
ejpam-3605	4	3	,	,	PUNCT
ejpam-3605	4	4	we	we	PRON
ejpam-3605	4	5	find	find	VERB
ejpam-3605	4	6	a	a	DET
ejpam-3605	4	7	criterion	criterion	NOUN
ejpam-3605	4	8	for	for	ADP
ejpam-3605	4	9	constructing	construct	VERB
ejpam-3605	4	10	an	an	DET
ejpam-3605	4	11	inscribed	inscribed	ADJ
ejpam-3605	4	12	hexagon	hexagon	NOUN
ejpam-3605	4	13	.	.	PUNCT
ejpam-3605	5	1	2020	2020	NUM
ejpam-3605	5	2	mathematics	mathematic	NOUN
ejpam-3605	5	3	subject	subject	NOUN
ejpam-3605	5	4	classifications	classification	NOUN
ejpam-3605	5	5	:	:	PUNCT
ejpam-3605	5	6	97g10	97g10	NUM
ejpam-3605	5	7	,	,	PUNCT
ejpam-3605	5	8	97g40	97g40	NUM
ejpam-3605	5	9	key	key	ADJ
ejpam-3605	5	10	words	word	NOUN
ejpam-3605	5	11	and	and	CCONJ
ejpam-3605	5	12	phrases	phrase	NOUN
ejpam-3605	5	13	:	:	PUNCT
ejpam-3605	5	14	ptolemy	ptolemy	PROPN
ejpam-3605	5	15	’s	’s	PART
ejpam-3605	5	16	theorem	theorem	PROPN
ejpam-3605	5	17	,	,	PUNCT
ejpam-3605	5	18	inscribed	inscribe	VERB
ejpam-3605	5	19	rectangle	rectangle	NOUN
ejpam-3605	5	20	,	,	PUNCT
ejpam-3605	5	21	regular	regular	ADJ
ejpam-3605	5	22	heptagon	heptagon	NOUN
ejpam-3605	5	23	,	,	PUNCT
ejpam-3605	5	24	inscribed	inscribe	VERB
ejpam-3605	5	25	hexagon	hexagon	PROPN
ejpam-3605	5	26	.	.	PUNCT
ejpam-3605	6	1	today	today	NOUN
ejpam-3605	6	2	,	,	PUNCT
ejpam-3605	6	3	to	to	PART
ejpam-3605	6	4	improve	improve	VERB
ejpam-3605	6	5	the	the	DET
ejpam-3605	6	6	quality	quality	NOUN
ejpam-3605	6	7	of	of	ADP
ejpam-3605	6	8	teaching	teaching	NOUN
ejpam-3605	6	9	mathematics	mathematic	NOUN
ejpam-3605	6	10	is	be	AUX
ejpam-3605	6	11	one	one	NUM
ejpam-3605	6	12	of	of	ADP
ejpam-3605	6	13	biggest	big	ADJ
ejpam-3605	6	14	challenges	challenge	NOUN
ejpam-3605	6	15	faced	face	VERB
ejpam-3605	6	16	in	in	ADP
ejpam-3605	6	17	the	the	DET
ejpam-3605	6	18	field	field	NOUN
ejpam-3605	6	19	of	of	ADP
ejpam-3605	6	20	education	education	NOUN
ejpam-3605	6	21	.	.	PUNCT
ejpam-3605	7	1	to	to	PART
ejpam-3605	7	2	do	do	VERB
ejpam-3605	7	3	so	so	ADV
ejpam-3605	7	4	,	,	PUNCT
ejpam-3605	7	5	you	you	PRON
ejpam-3605	7	6	have	have	VERB
ejpam-3605	7	7	to	to	PART
ejpam-3605	7	8	diversify	diversify	VERB
ejpam-3605	7	9	the	the	DET
ejpam-3605	7	10	process	process	NOUN
ejpam-3605	7	11	of	of	ADP
ejpam-3605	7	12	teaching	teaching	NOUN
ejpam-3605	7	13	,	,	PUNCT
ejpam-3605	7	14	to	to	PART
ejpam-3605	7	15	improve	improve	VERB
ejpam-3605	7	16	the	the	DET
ejpam-3605	7	17	methods	method	NOUN
ejpam-3605	7	18	of	of	ADP
ejpam-3605	7	19	teaching	teaching	NOUN
ejpam-3605	7	20	,	,	PUNCT
ejpam-3605	7	21	to	to	PART
ejpam-3605	7	22	start	start	VERB
ejpam-3605	7	23	using	use	VERB
ejpam-3605	7	24	new	new	ADJ
ejpam-3605	7	25	approaches	approach	NOUN
ejpam-3605	7	26	for	for	ADP
ejpam-3605	7	27	some	some	DET
ejpam-3605	7	28	problems	problem	NOUN
ejpam-3605	7	29	.	.	PUNCT
ejpam-3605	8	1	since	since	SCONJ
ejpam-3605	8	2	ancient	ancient	ADJ
ejpam-3605	8	3	times	time	NOUN
ejpam-3605	8	4	,	,	PUNCT
ejpam-3605	8	5	the	the	DET
ejpam-3605	8	6	researchers	researcher	NOUN
ejpam-3605	8	7	have	have	AUX
ejpam-3605	8	8	been	be	AUX
ejpam-3605	8	9	studying	study	VERB
ejpam-3605	8	10	the	the	DET
ejpam-3605	8	11	properties	property	NOUN
ejpam-3605	8	12	of	of	ADP
ejpam-3605	8	13	inscribed	inscribe	VERB
ejpam-3605	8	14	polygons	polygon	NOUN
ejpam-3605	8	15	.	.	PUNCT
ejpam-3605	9	1	the	the	DET
ejpam-3605	9	2	question	question	NOUN
ejpam-3605	9	3	of	of	ADP
ejpam-3605	9	4	”	"	PUNCT
ejpam-3605	9	5	under	under	ADP
ejpam-3605	9	6	what	what	DET
ejpam-3605	9	7	conditions	condition	NOUN
ejpam-3605	9	8	is	be	AUX
ejpam-3605	9	9	it	it	PRON
ejpam-3605	9	10	possible	possible	ADJ
ejpam-3605	9	11	to	to	PART
ejpam-3605	9	12	draw	draw	VERB
ejpam-3605	9	13	a	a	DET
ejpam-3605	9	14	polygon	polygon	NOUN
ejpam-3605	9	15	inside	inside	ADP
ejpam-3605	9	16	a	a	DET
ejpam-3605	9	17	circle	circle	NOUN
ejpam-3605	9	18	?	?	PUNCT
ejpam-3605	9	19	has	have	AUX
ejpam-3605	9	20	always	always	ADV
ejpam-3605	9	21	been	be	AUX
ejpam-3605	9	22	of	of	ADP
ejpam-3605	9	23	interest	interest	NOUN
ejpam-3605	9	24	,	,	PUNCT
ejpam-3605	9	25	and	and	CCONJ
ejpam-3605	9	26	some	some	DET
ejpam-3605	9	27	criteria	criterion	NOUN
ejpam-3605	9	28	were	be	AUX
ejpam-3605	9	29	found	find	VERB
ejpam-3605	9	30	for	for	ADP
ejpam-3605	9	31	inscribed	inscribe	VERB
ejpam-3605	9	32	polygons	polygon	NOUN
ejpam-3605	9	33	.	.	PUNCT
ejpam-3605	10	1	the	the	DET
ejpam-3605	10	2	criterion	criterion	NOUN
ejpam-3605	10	3	for	for	ADP
ejpam-3605	10	4	an	an	DET
ejpam-3605	10	5	inscribed	inscribe	VERB
ejpam-3605	10	6	rectangle	rectangle	NOUN
ejpam-3605	10	7	provided	provide	VERB
ejpam-3605	10	8	in	in	ADP
ejpam-3605	10	9	modern	modern	ADJ
ejpam-3605	10	10	textbooks	textbook	NOUN
ejpam-3605	10	11	of	of	ADP
ejpam-3605	10	12	secondary	secondary	ADJ
ejpam-3605	10	13	school	school	NOUN
ejpam-3605	10	14	geometry	geometry	NOUN
ejpam-3605	10	15	involves	involve	VERB
ejpam-3605	10	16	internal	internal	ADJ
ejpam-3605	10	17	angles	angle	NOUN
ejpam-3605	10	18	of	of	ADP
ejpam-3605	10	19	rectangle	rectangle	NOUN
ejpam-3605	10	20	.	.	PUNCT
ejpam-3605	11	1	it	it	PRON
ejpam-3605	11	2	says	say	VERB
ejpam-3605	11	3	:	:	PUNCT
ejpam-3605	11	4	for	for	SCONJ
ejpam-3605	11	5	a	a	DET
ejpam-3605	11	6	rectangle	rectangle	NOUN
ejpam-3605	11	7	to	to	PART
ejpam-3605	11	8	be	be	AUX
ejpam-3605	11	9	inscribed	inscribe	VERB
ejpam-3605	11	10	in	in	ADP
ejpam-3605	11	11	a	a	DET
ejpam-3605	11	12	circle	circle	NOUN
ejpam-3605	11	13	,	,	PUNCT
ejpam-3605	11	14	it	it	PRON
ejpam-3605	11	15	is	be	AUX
ejpam-3605	11	16	necessary	necessary	ADJ
ejpam-3605	11	17	and	and	CCONJ
ejpam-3605	11	18	sufficient	sufficient	ADJ
ejpam-3605	11	19	that	that	SCONJ
ejpam-3605	11	20	the	the	DET
ejpam-3605	11	21	sum	sum	NOUN
ejpam-3605	11	22	of	of	ADP
ejpam-3605	11	23	its	its	PRON
ejpam-3605	11	24	opposite	opposite	ADJ
ejpam-3605	11	25	angles	angle	NOUN
ejpam-3605	11	26	be	be	AUX
ejpam-3605	11	27	equal	equal	ADJ
ejpam-3605	11	28	to	to	ADP
ejpam-3605	11	29	180	180	NUM
ejpam-3605	11	30	◦	◦	NOUN
ejpam-3605	11	31	.	.	PUNCT
ejpam-3605	12	1	these	these	DET
ejpam-3605	12	2	textbooks	textbook	NOUN
ejpam-3605	12	3	do	do	AUX
ejpam-3605	12	4	not	not	PART
ejpam-3605	12	5	mention	mention	VERB
ejpam-3605	12	6	the	the	DET
ejpam-3605	12	7	relationships	relationship	NOUN
ejpam-3605	12	8	between	between	ADP
ejpam-3605	12	9	the	the	DET
ejpam-3605	12	10	sides	side	NOUN
ejpam-3605	12	11	and	and	CCONJ
ejpam-3605	12	12	diagonals	diagonal	NOUN
ejpam-3605	12	13	of	of	ADP
ejpam-3605	12	14	inscribed	inscribe	VERB
ejpam-3605	12	15	rectangle	rectangle	NOUN
ejpam-3605	12	16	.	.	PUNCT
ejpam-3605	13	1	though	though	ADV
ejpam-3605	13	2	,	,	PUNCT
ejpam-3605	13	3	this	this	PRON
ejpam-3605	13	4	is	be	AUX
ejpam-3605	13	5	exactly	exactly	ADV
ejpam-3605	13	6	what	what	PRON
ejpam-3605	13	7	ptolemy	ptolemy	NOUN
ejpam-3605	13	8	’s	’s	PART
ejpam-3605	13	9	famous	famous	ADJ
ejpam-3605	13	10	theorem	theorem	NOUN
ejpam-3605	13	11	is	be	AUX
ejpam-3605	13	12	about	about	ADP
ejpam-3605	13	13	.	.	PUNCT
ejpam-3605	14	1	not	not	PART
ejpam-3605	14	2	included	include	VERB
ejpam-3605	14	3	in	in	ADP
ejpam-3605	14	4	modern	modern	ADJ
ejpam-3605	14	5	school	school	NOUN
ejpam-3605	14	6	textbooks	textbook	NOUN
ejpam-3605	14	7	,	,	PUNCT
ejpam-3605	14	8	ptolemy	ptolemy	PROPN
ejpam-3605	14	9	’s	’s	PART
ejpam-3605	14	10	theorem	theorem	NOUN
ejpam-3605	14	11	is	be	AUX
ejpam-3605	14	12	a	a	DET
ejpam-3605	14	13	good	good	ADJ
ejpam-3605	14	14	criterion	criterion	NOUN
ejpam-3605	14	15	for	for	ADP
ejpam-3605	14	16	constructing	construct	VERB
ejpam-3605	14	17	an	an	DET
ejpam-3605	14	18	inscribed	inscribe	VERB
ejpam-3605	14	19	rectangle	rectangle	NOUN
ejpam-3605	14	20	which	which	PRON
ejpam-3605	14	21	involves	involve	VERB
ejpam-3605	14	22	the	the	DET
ejpam-3605	14	23	sides	side	NOUN
ejpam-3605	14	24	and	and	CCONJ
ejpam-3605	14	25	diagonals	diagonal	NOUN
ejpam-3605	14	26	of	of	ADP
ejpam-3605	14	27	a	a	DET
ejpam-3605	14	28	rectangle	rectangle	NOUN
ejpam-3605	14	29	.	.	PUNCT
ejpam-3605	15	1	it	it	PRON
ejpam-3605	15	2	says	say	VERB
ejpam-3605	15	3	:	:	PUNCT
ejpam-3605	15	4	for	for	SCONJ
ejpam-3605	15	5	a	a	DET
ejpam-3605	15	6	rectangle	rectangle	NOUN
ejpam-3605	15	7	to	to	PART
ejpam-3605	15	8	be	be	AUX
ejpam-3605	15	9	inscribed	inscribe	VERB
ejpam-3605	15	10	in	in	ADP
ejpam-3605	15	11	a	a	DET
ejpam-3605	15	12	circle	circle	NOUN
ejpam-3605	15	13	,	,	PUNCT
ejpam-3605	15	14	it	it	PRON
ejpam-3605	15	15	is	be	AUX
ejpam-3605	15	16	necessary	necessary	ADJ
ejpam-3605	15	17	and	and	CCONJ
ejpam-3605	15	18	sufficient	sufficient	ADJ
ejpam-3605	15	19	that	that	SCONJ
ejpam-3605	15	20	the	the	DET
ejpam-3605	15	21	sum	sum	NOUN
ejpam-3605	15	22	of	of	ADP
ejpam-3605	15	23	the	the	DET
ejpam-3605	15	24	products	product	NOUN
ejpam-3605	15	25	of	of	ADP
ejpam-3605	15	26	its	its	PRON
ejpam-3605	15	27	opposite	opposite	ADJ
ejpam-3605	15	28	sides	side	NOUN
ejpam-3605	15	29	be	be	VERB
ejpam-3605	15	30	equal	equal	ADJ
ejpam-3605	15	31	to	to	ADP
ejpam-3605	15	32	the	the	DET
ejpam-3605	15	33	product	product	NOUN
ejpam-3605	15	34	of	of	ADP
ejpam-3605	15	35	its	its	PRON
ejpam-3605	15	36	diagonals	diagonal	NOUN
ejpam-3605	15	37	.	.	PUNCT
ejpam-3605	16	1	in	in	ADP
ejpam-3605	16	2	this	this	DET
ejpam-3605	16	3	work	work	NOUN
ejpam-3605	16	4	,	,	PUNCT
ejpam-3605	16	5	we	we	PRON
ejpam-3605	16	6	consider	consider	VERB
ejpam-3605	16	7	some	some	DET
ejpam-3605	16	8	problems	problem	NOUN
ejpam-3605	16	9	which	which	PRON
ejpam-3605	16	10	have	have	AUX
ejpam-3605	16	11	been	be	AUX
ejpam-3605	16	12	earlier	early	ADV
ejpam-3605	16	13	solved	solve	VERB
ejpam-3605	16	14	by	by	ADP
ejpam-3605	16	15	traditional	traditional	ADJ
ejpam-3605	16	16	methods	method	NOUN
ejpam-3605	16	17	,	,	PUNCT
ejpam-3605	16	18	and	and	CCONJ
ejpam-3605	16	19	we	we	PRON
ejpam-3605	16	20	easily	easily	ADV
ejpam-3605	16	21	solve	solve	VERB
ejpam-3605	16	22	these	these	DET
ejpam-3605	16	23	problems	problem	NOUN
ejpam-3605	16	24	by	by	ADP
ejpam-3605	16	25	using	use	VERB
ejpam-3605	16	26	new	new	ADJ
ejpam-3605	16	27	approaches	approach	NOUN
ejpam-3605	16	28	,	,	PUNCT
ejpam-3605	16	29	namely	namely	ADV
ejpam-3605	16	30	,	,	PUNCT
ejpam-3605	16	31	ptolemy	ptolemy	PROPN
ejpam-3605	16	32	’s	’s	PART
ejpam-3605	16	33	theorem	theorem	PROPN
ejpam-3605	16	34	.	.	PUNCT
ejpam-3605	17	1	the	the	DET
ejpam-3605	17	2	results	result	NOUN
ejpam-3605	17	3	obtained	obtain	VERB
ejpam-3605	17	4	reveal	reveal	VERB
ejpam-3605	17	5	the	the	DET
ejpam-3605	17	6	effectiveness	effectiveness	NOUN
ejpam-3605	17	7	of	of	ADP
ejpam-3605	17	8	this	this	DET
ejpam-3605	17	9	new	new	ADJ
ejpam-3605	17	10	approach	approach	NOUN
ejpam-3605	17	11	.	.	PUNCT
ejpam-3605	18	1	it	it	PRON
ejpam-3605	18	2	incites	incite	VERB
ejpam-3605	18	3	students	student	NOUN
ejpam-3605	18	4	attention	attention	NOUN
ejpam-3605	18	5	to	to	ADP
ejpam-3605	18	6	the	the	DET
ejpam-3605	18	7	subjects	subject	NOUN
ejpam-3605	18	8	studied	study	VERB
ejpam-3605	18	9	during	during	ADP
ejpam-3605	18	10	geometry	geometry	NOUN
ejpam-3605	18	11	classes	class	NOUN
ejpam-3605	18	12	and	and	CCONJ
ejpam-3605	18	13	encourages	encourage	VERB
ejpam-3605	18	14	them	they	PRON
ejpam-3605	18	15	∗corresponding	∗corresponde	VERB
ejpam-3605	18	16	author	author	NOUN
ejpam-3605	18	17	.	.	PUNCT
ejpam-3605	19	1	doi	doi	NOUN
ejpam-3605	19	2	:	:	PUNCT
ejpam-3605	19	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3605	https://doi.org/10.29020/nybg.ejpam.v13i1.3605	NUM
ejpam-3605	19	4	email	email	NOUN
ejpam-3605	19	5	addresses	address	NOUN
ejpam-3605	19	6	:	:	PUNCT
ejpam-3605	19	7	samed59@bk.ru	samed59@bk.ru	PROPN
ejpam-3605	19	8	(	(	PUNCT
ejpam-3605	19	9	s.	s.	PROPN
ejpam-3605	19	10	j.aliyev	j.aliyev	PROPN
ejpam-3605	19	11	)	)	PUNCT
ejpam-3605	19	12	,	,	PUNCT
ejpam-3605	19	13	shalalahamidova@hotmail.com	shalalahamidova@hotmail.com	X
ejpam-3605	19	14	(	(	PUNCT
ejpam-3605	19	15	s.	s.	PROPN
ejpam-3605	19	16	a.hamidova	a.hamidova	PROPN
ejpam-3605	19	17	)	)	PUNCT
ejpam-3605	19	18	,	,	PUNCT
ejpam-3605	19	19	a.q.z.41@mail.ru	a.q.z.41@mail.ru	PROPN
ejpam-3605	19	20	(	(	PUNCT
ejpam-3605	19	21	g.	g.	PROPN
ejpam-3605	19	22	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3605	19	23	)	)	PUNCT
ejpam-3605	19	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3605	20	1	180	180	NUM
ejpam-3605	20	2	c	c	NOUN
ejpam-3605	20	3	©	©	NOUN
ejpam-3605	20	4	2020	2020	NUM
ejpam-3605	20	5	ejpam	ejpam	VERB
ejpam-3605	20	6	all	all	DET
ejpam-3605	20	7	rights	right	NOUN
ejpam-3605	20	8	reserved	reserve	VERB
ejpam-3605	20	9	.	.	PUNCT
ejpam-3605	21	1	s.	s.	PROPN
ejpam-3605	21	2	j.aliyev	j.aliyev	PROPN
ejpam-3605	21	3	,	,	PUNCT
ejpam-3605	21	4	s.	s.	PROPN
ejpam-3605	21	5	a.hamidova	a.hamidova	PROPN
ejpam-3605	21	6	,	,	PUNCT
ejpam-3605	21	7	g.	g.	PROPN
ejpam-3605	21	8	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3605	21	9	/	/	SYM
ejpam-3605	21	10	eur	eur	PROPN
ejpam-3605	21	11	.	.	PUNCT
ejpam-3605	22	1	j.	j.	PROPN
ejpam-3605	22	2	pure	pure	PROPN
ejpam-3605	22	3	appl	appl	PROPN
ejpam-3605	22	4	.	.	PROPN
ejpam-3605	22	5	math	math	PROPN
ejpam-3605	22	6	,	,	PUNCT
ejpam-3605	22	7	13	13	NUM
ejpam-3605	22	8	(	(	PUNCT
ejpam-3605	22	9	1	1	NUM
ejpam-3605	22	10	)	)	PUNCT
ejpam-3605	22	11	(	(	PUNCT
ejpam-3605	22	12	2020	2020	NUM
ejpam-3605	22	13	)	)	PUNCT
ejpam-3605	22	14	,	,	PUNCT
ejpam-3605	22	15	180	180	NUM
ejpam-3605	22	16	-	-	SYM
ejpam-3605	22	17	184	184	NUM
ejpam-3605	22	18	181	181	NUM
ejpam-3605	22	19	to	to	PART
ejpam-3605	22	20	learn	learn	VERB
ejpam-3605	22	21	more	more	ADJ
ejpam-3605	22	22	about	about	ADP
ejpam-3605	22	23	these	these	DET
ejpam-3605	22	24	subjects	subject	NOUN
ejpam-3605	22	25	.	.	PUNCT
ejpam-3605	23	1	as	as	ADP
ejpam-3605	23	2	a	a	DET
ejpam-3605	23	3	result	result	NOUN
ejpam-3605	23	4	,	,	PUNCT
ejpam-3605	23	5	students	student	NOUN
ejpam-3605	23	6	get	get	VERB
ejpam-3605	23	7	more	more	ADV
ejpam-3605	23	8	interested	interested	ADJ
ejpam-3605	23	9	in	in	ADP
ejpam-3605	23	10	geometry	geometry	NOUN
ejpam-3605	23	11	and	and	CCONJ
ejpam-3605	23	12	start	start	VERB
ejpam-3605	23	13	loving	love	VERB
ejpam-3605	23	14	it	it	PRON
ejpam-3605	23	15	.	.	PUNCT
ejpam-3605	24	1	inscribed	inscribe	VERB
ejpam-3605	24	2	polygons	polygon	NOUN
ejpam-3605	24	3	have	have	AUX
ejpam-3605	24	4	been	be	AUX
ejpam-3605	24	5	studied	study	VERB
ejpam-3605	24	6	in	in	ADP
ejpam-3605	24	7	[	[	X
ejpam-3605	24	8	1	1	NUM
ejpam-3605	24	9	]	]	PUNCT
ejpam-3605	24	10	,	,	PUNCT
ejpam-3605	24	11	[	[	X
ejpam-3605	24	12	2	2	NUM
ejpam-3605	24	13	]	]	PUNCT
ejpam-3605	24	14	,	,	PUNCT
ejpam-3605	24	15	[	[	X
ejpam-3605	24	16	5	5	NUM
ejpam-3605	24	17	]	]	PUNCT
ejpam-3605	24	18	.	.	PUNCT
ejpam-3605	25	1	also	also	ADV
ejpam-3605	25	2	,	,	PUNCT
ejpam-3605	25	3	the	the	DET
ejpam-3605	25	4	criteria	criterion	NOUN
ejpam-3605	25	5	for	for	ADP
ejpam-3605	25	6	constructing	construct	VERB
ejpam-3605	25	7	some	some	DET
ejpam-3605	25	8	inscribed	inscribe	VERB
ejpam-3605	25	9	polygons	polygon	NOUN
ejpam-3605	25	10	have	have	AUX
ejpam-3605	25	11	been	be	AUX
ejpam-3605	25	12	found	find	VERB
ejpam-3605	25	13	in	in	ADP
ejpam-3605	25	14	[	[	X
ejpam-3605	25	15	3	3	NUM
ejpam-3605	25	16	]	]	PUNCT
ejpam-3605	25	17	,	,	PUNCT
ejpam-3605	25	18	[	[	X
ejpam-3605	25	19	4	4	NUM
ejpam-3605	25	20	]	]	PUNCT
ejpam-3605	25	21	.	.	PUNCT
ejpam-3605	26	1	in	in	ADP
ejpam-3605	26	2	this	this	DET
ejpam-3605	26	3	work	work	NOUN
ejpam-3605	26	4	,	,	PUNCT
ejpam-3605	26	5	we	we	PRON
ejpam-3605	26	6	consider	consider	VERB
ejpam-3605	26	7	some	some	DET
ejpam-3605	26	8	applications	application	NOUN
ejpam-3605	26	9	of	of	ADP
ejpam-3605	26	10	ptolemy	ptolemy	PROPN
ejpam-3605	26	11	’s	’s	PART
ejpam-3605	26	12	theorem	theorem	PROPN
ejpam-3605	26	13	.	.	PUNCT
ejpam-3605	27	1	namely	namely	ADV
ejpam-3605	27	2	,	,	PUNCT
ejpam-3605	27	3	using	use	VERB
ejpam-3605	27	4	ptolemy	ptolemy	PROPN
ejpam-3605	27	5	’s	’s	PART
ejpam-3605	27	6	theorem	theorem	PROPN
ejpam-3605	27	7	,	,	PUNCT
ejpam-3605	27	8	1	1	NUM
ejpam-3605	27	9	)	)	PUNCT
ejpam-3605	27	10	we	we	PRON
ejpam-3605	27	11	prove	prove	VERB
ejpam-3605	27	12	some	some	DET
ejpam-3605	27	13	property	property	NOUN
ejpam-3605	27	14	of	of	ADP
ejpam-3605	27	15	a	a	DET
ejpam-3605	27	16	point	point	NOUN
ejpam-3605	27	17	lying	lie	VERB
ejpam-3605	27	18	on	on	ADP
ejpam-3605	27	19	a	a	DET
ejpam-3605	27	20	circle	circle	NOUN
ejpam-3605	27	21	circumscribed	circumscribe	VERB
ejpam-3605	27	22	about	about	ADP
ejpam-3605	27	23	some	some	DET
ejpam-3605	27	24	regular	regular	ADJ
ejpam-3605	27	25	triangle	triangle	NOUN
ejpam-3605	27	26	;	;	PUNCT
ejpam-3605	27	27	2	2	X
ejpam-3605	27	28	)	)	PUNCT
ejpam-3605	27	29	we	we	PRON
ejpam-3605	27	30	prove	prove	VERB
ejpam-3605	27	31	some	some	DET
ejpam-3605	27	32	property	property	NOUN
ejpam-3605	27	33	of	of	ADP
ejpam-3605	27	34	a	a	DET
ejpam-3605	27	35	regular	regular	ADJ
ejpam-3605	27	36	heptagon	heptagon	NOUN
ejpam-3605	27	37	;	;	PUNCT
ejpam-3605	27	38	3	3	X
ejpam-3605	27	39	)	)	PUNCT
ejpam-3605	27	40	we	we	PRON
ejpam-3605	27	41	find	find	VERB
ejpam-3605	27	42	a	a	DET
ejpam-3605	27	43	criterion	criterion	NOUN
ejpam-3605	27	44	for	for	ADP
ejpam-3605	27	45	constructing	construct	VERB
ejpam-3605	27	46	an	an	DET
ejpam-3605	27	47	inscribed	inscribed	ADJ
ejpam-3605	27	48	hexagon	hexagon	NOUN
ejpam-3605	27	49	.	.	PUNCT
ejpam-3605	28	1	we	we	PRON
ejpam-3605	28	2	first	first	ADV
ejpam-3605	28	3	prove	prove	VERB
ejpam-3605	28	4	that	that	SCONJ
ejpam-3605	28	5	if	if	SCONJ
ejpam-3605	28	6	the	the	DET
ejpam-3605	28	7	point	point	NOUN
ejpam-3605	28	8	m	m	VERB
ejpam-3605	28	9	lies	lie	VERB
ejpam-3605	28	10	on	on	ADP
ejpam-3605	28	11	a	a	DET
ejpam-3605	28	12	circle	circle	NOUN
ejpam-3605	28	13	circumscribed	circumscribe	VERB
ejpam-3605	28	14	about	about	ADP
ejpam-3605	28	15	the	the	DET
ejpam-3605	28	16	regular	regular	ADJ
ejpam-3605	28	17	triangle	triangle	NOUN
ejpam-3605	28	18	abc	abc	PROPN
ejpam-3605	28	19	,	,	PUNCT
ejpam-3605	28	20	then	then	ADV
ejpam-3605	28	21	one	one	NUM
ejpam-3605	28	22	of	of	ADP
ejpam-3605	28	23	the	the	DET
ejpam-3605	28	24	intervals	interval	NOUN
ejpam-3605	28	25	ma	ma	PROPN
ejpam-3605	28	26	,	,	PUNCT
ejpam-3605	28	27	mb	mb	PROPN
ejpam-3605	28	28	,	,	PUNCT
ejpam-3605	28	29	mc	mc	PROPN
ejpam-3605	28	30	is	be	AUX
ejpam-3605	28	31	equal	equal	ADJ
ejpam-3605	28	32	to	to	ADP
ejpam-3605	28	33	the	the	DET
ejpam-3605	28	34	sum	sum	NOUN
ejpam-3605	28	35	of	of	ADP
ejpam-3605	28	36	two	two	NUM
ejpam-3605	28	37	other	other	ADJ
ejpam-3605	28	38	intervals	interval	NOUN
ejpam-3605	28	39	.	.	PUNCT
ejpam-3605	29	1	figure	figure	NOUN
ejpam-3605	29	2	1	1	NUM
ejpam-3605	29	3	:	:	PUNCT
ejpam-3605	29	4	circle	circle	NOUN
ejpam-3605	29	5	circumscribed	circumscribe	VERB
ejpam-3605	29	6	about	about	ADP
ejpam-3605	29	7	the	the	DET
ejpam-3605	29	8	regular	regular	ADJ
ejpam-3605	29	9	triangle	triangle	NOUN
ejpam-3605	29	10	abc	abc	PROPN
ejpam-3605	29	11	.	.	PUNCT
ejpam-3605	30	1	let	let	VERB
ejpam-3605	30	2	the	the	DET
ejpam-3605	30	3	point	point	NOUN
ejpam-3605	30	4	m	m	AUX
ejpam-3605	30	5	lie	lie	VERB
ejpam-3605	30	6	on	on	ADP
ejpam-3605	30	7	the	the	DET
ejpam-3605	30	8	arc	arc	NOUN
ejpam-3605	31	1	ab	ab	PROPN
ejpam-3605	31	2	(	(	PUNCT
ejpam-3605	31	3	figure	figure	NOUN
ejpam-3605	31	4	1	1	NUM
ejpam-3605	31	5	)	)	PUNCT
ejpam-3605	31	6	.	.	PUNCT
ejpam-3605	32	1	let	let	VERB
ejpam-3605	32	2	’s	’s	PRON
ejpam-3605	32	3	prove	prove	VERB
ejpam-3605	32	4	that	that	SCONJ
ejpam-3605	32	5	ma	ma	PROPN
ejpam-3605	32	6	+	+	CCONJ
ejpam-3605	32	7	mb	mb	PROPN
ejpam-3605	32	8	=	=	PROPN
ejpam-3605	32	9	mc	mc	PROPN
ejpam-3605	32	10	.	.	PROPN
ejpam-3605	33	1	(	(	PUNCT
ejpam-3605	33	2	1	1	X
ejpam-3605	33	3	)	)	PUNCT
ejpam-3605	33	4	we	we	PRON
ejpam-3605	33	5	will	will	AUX
ejpam-3605	33	6	use	use	VERB
ejpam-3605	33	7	traditional	traditional	ADJ
ejpam-3605	33	8	methods	method	NOUN
ejpam-3605	33	9	.	.	PUNCT
ejpam-3605	34	1	as	as	ADP
ejpam-3605	34	2	∠bmc	∠bmc	PROPN
ejpam-3605	34	3	=	=	SYM
ejpam-3605	34	4	∠cma	∠cma	PROPN
ejpam-3605	34	5	,	,	PUNCT
ejpam-3605	34	6	due	due	ADP
ejpam-3605	34	7	to	to	ADP
ejpam-3605	34	8	angle	angle	NOUN
ejpam-3605	34	9	bisector	bisector	NOUN
ejpam-3605	34	10	property	property	NOUN
ejpam-3605	34	11	of	of	ADP
ejpam-3605	34	12	a	a	DET
ejpam-3605	34	13	triangle	triangle	NOUN
ejpam-3605	34	14	we	we	PRON
ejpam-3605	34	15	have	have	VERB
ejpam-3605	34	16	mb	mb	ADP
ejpam-3605	34	17	ma	ma	PROPN
ejpam-3605	34	18	=	=	PROPN
ejpam-3605	34	19	bk	bk	PROPN
ejpam-3605	34	20	ka	ka	PROPN
ejpam-3605	34	21	or	or	CCONJ
ejpam-3605	34	22	bk	bk	PROPN
ejpam-3605	34	23	·	·	PUNCT
ejpam-3605	34	24	ma	ma	PROPN
ejpam-3605	34	25	=	=	PUNCT
ejpam-3605	34	26	mb	mb	PROPN
ejpam-3605	34	27	·	·	PROPN
ejpam-3605	34	28	ka	ka	PROPN
ejpam-3605	34	29	,	,	PUNCT
ejpam-3605	34	30	(	(	PUNCT
ejpam-3605	34	31	2	2	NUM
ejpam-3605	34	32	)	)	PUNCT
ejpam-3605	34	33	regarding	regard	VERB
ejpam-3605	34	34	similar	similar	ADJ
ejpam-3605	34	35	triangles	triangle	NOUN
ejpam-3605	34	36	bmc	bmc	NOUN
ejpam-3605	34	37	and	and	CCONJ
ejpam-3605	34	38	kma	kma	PROPN
ejpam-3605	34	39	,	,	PUNCT
ejpam-3605	34	40	we	we	PRON
ejpam-3605	34	41	have	have	VERB
ejpam-3605	34	42	bc	bc	PROPN
ejpam-3605	34	43	ka	ka	PROPN
ejpam-3605	35	1	=	=	PROPN
ejpam-3605	35	2	mc	mc	PROPN
ejpam-3605	35	3	ma	ma	PROPN
ejpam-3605	35	4	or	or	CCONJ
ejpam-3605	35	5	bc	bc	PROPN
ejpam-3605	35	6	·	·	SYM
ejpam-3605	35	7	ma	ma	PROPN
ejpam-3605	35	8	=	=	PROPN
ejpam-3605	35	9	mc	mc	PROPN
ejpam-3605	35	10	·	·	SYM
ejpam-3605	35	11	ka	ka	PROPN
ejpam-3605	35	12	,	,	PUNCT
ejpam-3605	35	13	as	as	ADP
ejpam-3605	35	14	bc	bc	PROPN
ejpam-3605	35	15	=	=	PUNCT
ejpam-3605	35	16	bk	bk	PROPN
ejpam-3605	35	17	+	+	PROPN
ejpam-3605	35	18	ka	ka	PROPN
ejpam-3605	35	19	,	,	PUNCT
ejpam-3605	35	20	from	from	ADP
ejpam-3605	35	21	the	the	DET
ejpam-3605	35	22	last	last	ADJ
ejpam-3605	35	23	equality	equality	NOUN
ejpam-3605	35	24	,	,	PUNCT
ejpam-3605	35	25	using	use	VERB
ejpam-3605	35	26	(	(	PUNCT
ejpam-3605	35	27	2	2	NUM
ejpam-3605	35	28	)	)	PUNCT
ejpam-3605	35	29	,	,	PUNCT
ejpam-3605	35	30	we	we	PRON
ejpam-3605	35	31	get	get	VERB
ejpam-3605	35	32	the	the	DET
ejpam-3605	35	33	validity	validity	NOUN
ejpam-3605	35	34	of	of	ADP
ejpam-3605	35	35	(	(	PUNCT
ejpam-3605	35	36	1	1	NUM
ejpam-3605	35	37	):	):	PUNCT
ejpam-3605	35	38	(	(	PUNCT
ejpam-3605	35	39	bk	bk	PROPN
ejpam-3605	35	40	+	+	PROPN
ejpam-3605	35	41	ka	ka	PROPN
ejpam-3605	35	42	)	)	PUNCT
ejpam-3605	35	43	·	·	PUNCT
ejpam-3605	35	44	ma	ma	PROPN
ejpam-3605	35	45	=	=	SYM
ejpam-3605	35	46	mc	mc	PROPN
ejpam-3605	35	47	·	·	PROPN
ejpam-3605	35	48	ka	ka	PROPN
ejpam-3605	35	49	s.	s.	PROPN
ejpam-3605	35	50	j.aliyev	j.aliyev	PROPN
ejpam-3605	35	51	,	,	PUNCT
ejpam-3605	35	52	s.	s.	PROPN
ejpam-3605	35	53	a.hamidova	a.hamidova	PROPN
ejpam-3605	35	54	,	,	PUNCT
ejpam-3605	35	55	g.	g.	PROPN
ejpam-3605	35	56	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3605	35	57	/	/	SYM
ejpam-3605	35	58	eur	eur	PROPN
ejpam-3605	35	59	.	.	PUNCT
ejpam-3605	36	1	j.	j.	PROPN
ejpam-3605	36	2	pure	pure	PROPN
ejpam-3605	36	3	appl	appl	PROPN
ejpam-3605	36	4	.	.	PROPN
ejpam-3605	36	5	math	math	PROPN
ejpam-3605	36	6	,	,	PUNCT
ejpam-3605	36	7	13	13	NUM
ejpam-3605	36	8	(	(	PUNCT
ejpam-3605	36	9	1	1	NUM
ejpam-3605	36	10	)	)	PUNCT
ejpam-3605	36	11	(	(	PUNCT
ejpam-3605	36	12	2020	2020	NUM
ejpam-3605	36	13	)	)	PUNCT
ejpam-3605	36	14	,	,	PUNCT
ejpam-3605	36	15	180	180	NUM
ejpam-3605	36	16	-	-	SYM
ejpam-3605	36	17	184	184	NUM
ejpam-3605	36	18	182	182	NUM
ejpam-3605	36	19	bk	bk	ADP
ejpam-3605	36	20	·	·	PUNCT
ejpam-3605	36	21	ma	ma	PROPN
ejpam-3605	36	22	+	+	CCONJ
ejpam-3605	36	23	ma	ma	PROPN
ejpam-3605	36	24	·	·	PROPN
ejpam-3605	36	25	ka	ka	PROPN
ejpam-3605	36	26	=	=	PROPN
ejpam-3605	36	27	mc	mc	PROPN
ejpam-3605	36	28	·	·	SYM
ejpam-3605	36	29	ka	ka	PROPN
ejpam-3605	36	30	,	,	PUNCT
ejpam-3605	36	31	mb	mb	PROPN
ejpam-3605	36	32	·	·	PROPN
ejpam-3605	36	33	ka	ka	PROPN
ejpam-3605	36	34	+	+	CCONJ
ejpam-3605	36	35	ma	ma	PROPN
ejpam-3605	36	36	·	·	PROPN
ejpam-3605	36	37	ka	ka	PROPN
ejpam-3605	37	1	=	=	PROPN
ejpam-3605	37	2	mc	mc	PROPN
ejpam-3605	37	3	·	·	SYM
ejpam-3605	37	4	ka	ka	PROPN
ejpam-3605	37	5	,	,	PUNCT
ejpam-3605	37	6	or	or	CCONJ
ejpam-3605	37	7	mb	mb	ADP
ejpam-3605	37	8	+	+	CCONJ
ejpam-3605	37	9	ma	ma	PROPN
ejpam-3605	37	10	=	=	PROPN
ejpam-3605	37	11	mc	mc	PROPN
ejpam-3605	37	12	.	.	PUNCT
ejpam-3605	38	1	but	but	CCONJ
ejpam-3605	38	2	,	,	PUNCT
ejpam-3605	38	3	this	this	DET
ejpam-3605	38	4	relation	relation	NOUN
ejpam-3605	38	5	can	can	AUX
ejpam-3605	38	6	be	be	AUX
ejpam-3605	38	7	obtained	obtain	VERB
ejpam-3605	38	8	quite	quite	ADV
ejpam-3605	38	9	easily	easily	ADV
ejpam-3605	38	10	without	without	ADP
ejpam-3605	38	11	using	use	VERB
ejpam-3605	38	12	bisector	bisector	NOUN
ejpam-3605	38	13	property	property	NOUN
ejpam-3605	38	14	and	and	CCONJ
ejpam-3605	38	15	similar	similar	ADJ
ejpam-3605	38	16	triangles	triangle	NOUN
ejpam-3605	38	17	,	,	PUNCT
ejpam-3605	38	18	just	just	ADV
ejpam-3605	38	19	by	by	ADP
ejpam-3605	38	20	means	mean	NOUN
ejpam-3605	38	21	of	of	ADP
ejpam-3605	38	22	ptolemy	ptolemy	PROPN
ejpam-3605	38	23	’s	’s	PART
ejpam-3605	38	24	theorem	theorem	PROPN
ejpam-3605	38	25	.	.	PROPN
ejpam-3605	39	1	as	as	SCONJ
ejpam-3605	39	2	the	the	DET
ejpam-3605	39	3	rectangle	rectangle	NOUN
ejpam-3605	39	4	mabc	mabc	NOUN
ejpam-3605	39	5	is	be	AUX
ejpam-3605	39	6	inscribed	inscribe	VERB
ejpam-3605	39	7	,	,	PUNCT
ejpam-3605	39	8	by	by	ADP
ejpam-3605	39	9	ptolemy	ptolemy	PROPN
ejpam-3605	39	10	’s	’s	PART
ejpam-3605	39	11	theorem	theorem	NOUN
ejpam-3605	39	12	we	we	PRON
ejpam-3605	39	13	have	have	VERB
ejpam-3605	39	14	ma	ma	PROPN
ejpam-3605	39	15	·	·	PROPN
ejpam-3605	39	16	bc	bc	PROPN
ejpam-3605	39	17	+	+	CCONJ
ejpam-3605	39	18	mb	mb	PROPN
ejpam-3605	39	19	·	·	PUNCT
ejpam-3605	39	20	ac	ac	PROPN
ejpam-3605	39	21	=	=	PUNCT
ejpam-3605	39	22	mc	mc	PROPN
ejpam-3605	39	23	·	·	PUNCT
ejpam-3605	39	24	ab	ab	PROPN
ejpam-3605	39	25	.	.	PUNCT
ejpam-3605	40	1	considering	consider	VERB
ejpam-3605	40	2	the	the	DET
ejpam-3605	40	3	conditions	condition	NOUN
ejpam-3605	40	4	bc	bc	PROPN
ejpam-3605	40	5	=	=	SYM
ejpam-3605	40	6	ac	ac	PROPN
ejpam-3605	40	7	=	=	PROPN
ejpam-3605	40	8	ab	ab	PROPN
ejpam-3605	40	9	,	,	PUNCT
ejpam-3605	40	10	we	we	PRON
ejpam-3605	40	11	get	get	VERB
ejpam-3605	40	12	the	the	DET
ejpam-3605	40	13	validity	validity	NOUN
ejpam-3605	40	14	of	of	ADP
ejpam-3605	40	15	(	(	PUNCT
ejpam-3605	40	16	1	1	NUM
ejpam-3605	40	17	)	)	PUNCT
ejpam-3605	40	18	.	.	PUNCT
ejpam-3605	41	1	now	now	ADV
ejpam-3605	41	2	let	let	VERB
ejpam-3605	41	3	’s	’s	NOUN
ejpam-3605	41	4	prove	prove	VERB
ejpam-3605	41	5	that	that	SCONJ
ejpam-3605	41	6	if	if	SCONJ
ejpam-3605	41	7	the	the	DET
ejpam-3605	41	8	points	point	NOUN
ejpam-3605	41	9	a	a	DET
ejpam-3605	41	10	,	,	PUNCT
ejpam-3605	41	11	b	b	NOUN
ejpam-3605	41	12	,	,	PUNCT
ejpam-3605	41	13	c	c	NOUN
ejpam-3605	41	14	,	,	PUNCT
ejpam-3605	41	15	d	d	X
ejpam-3605	41	16	are	be	AUX
ejpam-3605	41	17	the	the	DET
ejpam-3605	41	18	consecutive	consecutive	ADJ
ejpam-3605	41	19	vertices	vertex	NOUN
ejpam-3605	41	20	of	of	ADP
ejpam-3605	41	21	a	a	DET
ejpam-3605	41	22	regular	regular	ADJ
ejpam-3605	41	23	heptagon	heptagon	NOUN
ejpam-3605	41	24	(	(	PUNCT
ejpam-3605	41	25	figure	figure	NOUN
ejpam-3605	41	26	2	2	NUM
ejpam-3605	41	27	)	)	PUNCT
ejpam-3605	41	28	,	,	PUNCT
ejpam-3605	41	29	then	then	ADV
ejpam-3605	41	30	the	the	DET
ejpam-3605	41	31	following	follow	VERB
ejpam-3605	41	32	relation	relation	NOUN
ejpam-3605	41	33	holds	hold	VERB
ejpam-3605	41	34	:	:	PUNCT
ejpam-3605	41	35	1	1	NUM
ejpam-3605	41	36	ab	ab	NOUN
ejpam-3605	41	37	=	=	SYM
ejpam-3605	41	38	1	1	NUM
ejpam-3605	41	39	ac	ac	NOUN
ejpam-3605	41	40	+	+	CCONJ
ejpam-3605	41	41	1	1	NUM
ejpam-3605	41	42	ad	ad	NOUN
ejpam-3605	41	43	.	.	PUNCT
ejpam-3605	42	1	(	(	PUNCT
ejpam-3605	42	2	3	3	X
ejpam-3605	42	3	)	)	PUNCT
ejpam-3605	42	4	figure	figure	NOUN
ejpam-3605	42	5	2	2	NUM
ejpam-3605	42	6	:	:	PUNCT
ejpam-3605	42	7	regular	regular	ADJ
ejpam-3605	42	8	heptaqon	heptaqon	NOUN
ejpam-3605	42	9	abcdefk	abcdefk	NOUN
ejpam-3605	42	10	.	.	PUNCT
ejpam-3605	43	1	let	let	VERB
ejpam-3605	43	2	the	the	DET
ejpam-3605	43	3	point	point	NOUN
ejpam-3605	43	4	e	e	NOUN
ejpam-3605	43	5	be	be	AUX
ejpam-3605	43	6	a	a	DET
ejpam-3605	43	7	vertex	vertex	NOUN
ejpam-3605	43	8	of	of	ADP
ejpam-3605	43	9	a	a	DET
ejpam-3605	43	10	regular	regular	ADJ
ejpam-3605	43	11	heptagon	heptagon	NOUN
ejpam-3605	43	12	next	next	ADV
ejpam-3605	43	13	to	to	ADP
ejpam-3605	43	14	d.	d.	PROPN
ejpam-3605	43	15	the	the	DET
ejpam-3605	43	16	triangles	triangle	NOUN
ejpam-3605	43	17	abc	abc	PROPN
ejpam-3605	43	18	and	and	CCONJ
ejpam-3605	43	19	acd	acd	NOUN
ejpam-3605	43	20	are	be	AUX
ejpam-3605	43	21	equal	equal	ADJ
ejpam-3605	43	22	to	to	ADP
ejpam-3605	43	23	the	the	DET
ejpam-3605	43	24	triangles	triangle	NOUN
ejpam-3605	43	25	cde	cde	PROPN
ejpam-3605	43	26	and	and	CCONJ
ejpam-3605	43	27	afe	afe	PROPN
ejpam-3605	43	28	,	,	PUNCT
ejpam-3605	43	29	respectively	respectively	ADV
ejpam-3605	43	30	.	.	PUNCT
ejpam-3605	44	1	hence	hence	ADV
ejpam-3605	44	2	ac	ac	PROPN
ejpam-3605	44	3	=	=	SYM
ejpam-3605	44	4	ce	ce	PROPN
ejpam-3605	44	5	and	and	CCONJ
ejpam-3605	44	6	ad	ad	NOUN
ejpam-3605	44	7	=	=	SYM
ejpam-3605	44	8	ae	ae	PROPN
ejpam-3605	44	9	.	.	PUNCT
ejpam-3605	45	1	taking	take	VERB
ejpam-3605	45	2	into	into	ADP
ejpam-3605	45	3	account	account	NOUN
ejpam-3605	45	4	the	the	DET
ejpam-3605	45	5	equality	equality	NOUN
ejpam-3605	45	6	of	of	ADP
ejpam-3605	45	7	these	these	DET
ejpam-3605	45	8	intervals	interval	NOUN
ejpam-3605	45	9	and	and	CCONJ
ejpam-3605	45	10	the	the	DET
ejpam-3605	45	11	conditions	condition	NOUN
ejpam-3605	45	12	de	de	X
ejpam-3605	45	13	=	=	SYM
ejpam-3605	45	14	cd	cd	PROPN
ejpam-3605	45	15	=	=	SYM
ejpam-3605	45	16	ab	ab	PROPN
ejpam-3605	45	17	,	,	PUNCT
ejpam-3605	45	18	by	by	ADP
ejpam-3605	45	19	ptolemy	ptolemy	PROPN
ejpam-3605	45	20	’s	’s	PART
ejpam-3605	45	21	theorem	theorem	PROPN
ejpam-3605	45	22	applied	apply	VERB
ejpam-3605	45	23	to	to	ADP
ejpam-3605	45	24	the	the	DET
ejpam-3605	45	25	rectangle	rectangle	NOUN
ejpam-3605	45	26	acde	acde	ADP
ejpam-3605	45	27	we	we	PRON
ejpam-3605	45	28	get	get	VERB
ejpam-3605	45	29	the	the	DET
ejpam-3605	45	30	validity	validity	NOUN
ejpam-3605	45	31	of	of	ADP
ejpam-3605	45	32	(	(	PUNCT
ejpam-3605	45	33	3	3	NUM
ejpam-3605	45	34	):	):	PUNCT
ejpam-3605	45	35	ac	ac	PROPN
ejpam-3605	45	36	·	·	PUNCT
ejpam-3605	45	37	de	de	X
ejpam-3605	45	38	+	+	CCONJ
ejpam-3605	45	39	ae	ae	PROPN
ejpam-3605	45	40	·	·	PUNCT
ejpam-3605	45	41	cd	cd	PROPN
ejpam-3605	45	42	=	=	SYM
ejpam-3605	45	43	ce	ce	PROPN
ejpam-3605	45	44	·	·	SYM
ejpam-3605	45	45	ad	ad	NOUN
ejpam-3605	45	46	,	,	PUNCT
ejpam-3605	45	47	ac	ac	PROPN
ejpam-3605	45	48	·	·	PROPN
ejpam-3605	45	49	ab	ab	PROPN
ejpam-3605	45	50	+	+	CCONJ
ejpam-3605	45	51	ad	ad	NOUN
ejpam-3605	45	52	·	·	PUNCT
ejpam-3605	45	53	ab	ab	PROPN
ejpam-3605	45	54	=	=	PUNCT
ejpam-3605	45	55	ac	ac	PROPN
ejpam-3605	45	56	·	·	PROPN
ejpam-3605	45	57	ad	ad	NOUN
ejpam-3605	45	58	,	,	PUNCT
ejpam-3605	45	59	1	1	NUM
ejpam-3605	45	60	ab	ab	NOUN
ejpam-3605	45	61	=	=	SYM
ejpam-3605	45	62	1	1	NUM
ejpam-3605	45	63	ac	ac	NOUN
ejpam-3605	45	64	+	+	CCONJ
ejpam-3605	45	65	1	1	NUM
ejpam-3605	45	66	ad	ad	NOUN
ejpam-3605	45	67	.	.	PUNCT
ejpam-3605	46	1	finally	finally	ADV
ejpam-3605	46	2	,	,	PUNCT
ejpam-3605	46	3	let	let	VERB
ejpam-3605	46	4	’s	’s	PRON
ejpam-3605	46	5	find	find	VERB
ejpam-3605	46	6	a	a	DET
ejpam-3605	46	7	criterion	criterion	NOUN
ejpam-3605	46	8	for	for	ADP
ejpam-3605	46	9	constructing	construct	VERB
ejpam-3605	46	10	an	an	DET
ejpam-3605	46	11	inscribed	inscribed	ADJ
ejpam-3605	46	12	hexagon	hexagon	NOUN
ejpam-3605	46	13	,	,	PUNCT
ejpam-3605	46	14	which	which	PRON
ejpam-3605	46	15	involves	involve	VERB
ejpam-3605	46	16	its	its	PRON
ejpam-3605	46	17	sides	side	NOUN
ejpam-3605	46	18	and	and	CCONJ
ejpam-3605	46	19	large	large	ADJ
ejpam-3605	46	20	diagonals	diagonal	NOUN
ejpam-3605	46	21	,	,	PUNCT
ejpam-3605	46	22	using	use	VERB
ejpam-3605	46	23	ptolemy	ptolemy	PROPN
ejpam-3605	46	24	’s	’s	PART
ejpam-3605	46	25	theorem	theorem	PROPN
ejpam-3605	46	26	.	.	PUNCT
ejpam-3605	47	1	in	in	ADP
ejpam-3605	47	2	other	other	ADJ
ejpam-3605	47	3	words	word	NOUN
ejpam-3605	47	4	,	,	PUNCT
ejpam-3605	47	5	let	let	VERB
ejpam-3605	47	6	’s	’s	PRON
ejpam-3605	47	7	prove	prove	VERB
ejpam-3605	47	8	that	that	SCONJ
ejpam-3605	47	9	the	the	DET
ejpam-3605	47	10	product	product	NOUN
ejpam-3605	47	11	of	of	ADP
ejpam-3605	47	12	large	large	ADJ
ejpam-3605	47	13	diagonals	diagonal	NOUN
ejpam-3605	47	14	of	of	ADP
ejpam-3605	47	15	an	an	DET
ejpam-3605	47	16	inscribed	inscribe	VERB
ejpam-3605	47	17	hexagon	hexagon	NOUN
ejpam-3605	47	18	is	be	AUX
ejpam-3605	47	19	equal	equal	ADJ
ejpam-3605	47	20	to	to	ADP
ejpam-3605	47	21	the	the	DET
ejpam-3605	47	22	sum	sum	NOUN
ejpam-3605	47	23	of	of	ADP
ejpam-3605	47	24	products	product	NOUN
ejpam-3605	47	25	of	of	ADP
ejpam-3605	47	26	its	its	PRON
ejpam-3605	47	27	s.	s.	PROPN
ejpam-3605	47	28	j.aliyev	j.aliyev	PROPN
ejpam-3605	47	29	,	,	PUNCT
ejpam-3605	47	30	s.	s.	PROPN
ejpam-3605	47	31	a.hamidova	a.hamidova	PROPN
ejpam-3605	47	32	,	,	PUNCT
ejpam-3605	47	33	g.	g.	PROPN
ejpam-3605	47	34	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3605	47	35	/	/	SYM
ejpam-3605	47	36	eur	eur	PROPN
ejpam-3605	47	37	.	.	PUNCT
ejpam-3605	48	1	j.	j.	PROPN
ejpam-3605	48	2	pure	pure	PROPN
ejpam-3605	48	3	appl	appl	PROPN
ejpam-3605	48	4	.	.	PROPN
ejpam-3605	48	5	math	math	PROPN
ejpam-3605	48	6	,	,	PUNCT
ejpam-3605	48	7	13	13	NUM
ejpam-3605	48	8	(	(	PUNCT
ejpam-3605	48	9	1	1	NUM
ejpam-3605	48	10	)	)	PUNCT
ejpam-3605	48	11	(	(	PUNCT
ejpam-3605	48	12	2020	2020	NUM
ejpam-3605	48	13	)	)	PUNCT
ejpam-3605	48	14	,	,	PUNCT
ejpam-3605	48	15	180	180	NUM
ejpam-3605	48	16	-	-	SYM
ejpam-3605	48	17	184	184	NUM
ejpam-3605	48	18	183	183	NUM
ejpam-3605	48	19	consecutive	consecutive	ADJ
ejpam-3605	48	20	non	non	ADJ
ejpam-3605	48	21	-	-	ADJ
ejpam-3605	48	22	adjacent	adjacent	ADJ
ejpam-3605	48	23	sides	side	NOUN
ejpam-3605	48	24	and	and	CCONJ
ejpam-3605	48	25	products	product	NOUN
ejpam-3605	48	26	of	of	ADP
ejpam-3605	48	27	its	its	PRON
ejpam-3605	48	28	opposite	opposite	ADJ
ejpam-3605	48	29	sides	side	NOUN
ejpam-3605	48	30	with	with	ADP
ejpam-3605	48	31	a	a	DET
ejpam-3605	48	32	large	large	ADJ
ejpam-3605	48	33	diagonal	diagonal	NOUN
ejpam-3605	48	34	which	which	PRON
ejpam-3605	48	35	does	do	AUX
ejpam-3605	48	36	not	not	PART
ejpam-3605	48	37	intersect	intersect	VERB
ejpam-3605	48	38	any	any	PRON
ejpam-3605	48	39	of	of	ADP
ejpam-3605	48	40	these	these	DET
ejpam-3605	48	41	sides	side	NOUN
ejpam-3605	48	42	.	.	PUNCT
ejpam-3605	49	1	let	let	VERB
ejpam-3605	49	2	the	the	DET
ejpam-3605	49	3	hexagon	hexagon	NOUN
ejpam-3605	49	4	abca1b1c1	abca1b1c1	NOUN
ejpam-3605	49	5	be	be	AUX
ejpam-3605	49	6	inscribed	inscribe	VERB
ejpam-3605	49	7	in	in	ADP
ejpam-3605	49	8	a	a	DET
ejpam-3605	49	9	circle	circle	NOUN
ejpam-3605	49	10	(	(	PUNCT
ejpam-3605	49	11	figure	figure	NOUN
ejpam-3605	49	12	3	3	NUM
ejpam-3605	49	13	)	)	PUNCT
ejpam-3605	49	14	.	.	PUNCT
ejpam-3605	50	1	figure	figure	VERB
ejpam-3605	50	2	3	3	NUM
ejpam-3605	50	3	:	:	PUNCT
ejpam-3605	50	4	the	the	DET
ejpam-3605	50	5	hexagon	hexagon	NOUN
ejpam-3605	50	6	abca1b1c1	abca1b1c1	NOUN
ejpam-3605	50	7	be	be	AUX
ejpam-3605	50	8	inscribed	inscribe	VERB
ejpam-3605	50	9	in	in	ADP
ejpam-3605	50	10	a	a	DET
ejpam-3605	50	11	circle	circle	NOUN
ejpam-3605	50	12	.	.	PUNCT
ejpam-3605	51	1	we	we	PRON
ejpam-3605	51	2	must	must	AUX
ejpam-3605	51	3	prove	prove	VERB
ejpam-3605	51	4	that	that	SCONJ
ejpam-3605	51	5	the	the	DET
ejpam-3605	51	6	following	follow	VERB
ejpam-3605	51	7	relation	relation	NOUN
ejpam-3605	51	8	is	be	AUX
ejpam-3605	51	9	true	true	ADJ
ejpam-3605	51	10	in	in	ADP
ejpam-3605	51	11	the	the	DET
ejpam-3605	51	12	hexagon	hexagon	NOUN
ejpam-3605	51	13	abca1b1c1	abca1b1c1	PROPN
ejpam-3605	51	14	:	:	PUNCT
ejpam-3605	51	15	aa1	aa1	PROPN
ejpam-3605	51	16	·	·	PUNCT
ejpam-3605	51	17	bb1	bb1	PROPN
ejpam-3605	51	18	·	·	PUNCT
ejpam-3605	51	19	cc1	cc1	NOUN
ejpam-3605	51	20	=	=	SYM
ejpam-3605	51	21	ab	ab	PROPN
ejpam-3605	51	22	·	·	PUNCT
ejpam-3605	51	23	ca1	ca1	PROPN
ejpam-3605	51	24	·	·	PUNCT
ejpam-3605	51	25	b1c1	b1c1	X
ejpam-3605	51	26	+	+	NUM
ejpam-3605	52	1	bc	bc	PROPN
ejpam-3605	52	2	·	·	PUNCT
ejpam-3605	52	3	a1b1	a1b1	PROPN
ejpam-3605	52	4	·	·	PUNCT
ejpam-3605	52	5	ac1	ac1	PROPN
ejpam-3605	52	6	+	+	PROPN
ejpam-3605	52	7	+	+	ADJ
ejpam-3605	52	8	ab	ab	PROPN
ejpam-3605	52	9	·	·	PUNCT
ejpam-3605	52	10	a1b1	a1b1	X
ejpam-3605	52	11	·	·	PUNCT
ejpam-3605	52	12	cc1	cc1	PROPN
ejpam-3605	52	13	+	+	CCONJ
ejpam-3605	52	14	bc	bc	PROPN
ejpam-3605	52	15	·	·	PUNCT
ejpam-3605	52	16	b1c1	b1c1	X
ejpam-3605	52	17	·	·	PUNCT
ejpam-3605	52	18	aa1	aa1	PROPN
ejpam-3605	52	19	+	+	CCONJ
ejpam-3605	52	20	ca1	ca1	PROPN
ejpam-3605	52	21	·	·	PUNCT
ejpam-3605	52	22	ac1	ac1	PROPN
ejpam-3605	52	23	·	·	SYM
ejpam-3605	52	24	bb1	bb1	PROPN
ejpam-3605	52	25	.	.	PUNCT
ejpam-3605	53	1	(	(	PUNCT
ejpam-3605	53	2	4	4	X
ejpam-3605	53	3	)	)	PUNCT
ejpam-3605	53	4	applying	apply	VERB
ejpam-3605	53	5	ptolemy	ptolemy	NOUN
ejpam-3605	53	6	’s	’s	PART
ejpam-3605	53	7	theorem	theorem	NOUN
ejpam-3605	53	8	to	to	ADP
ejpam-3605	53	9	the	the	DET
ejpam-3605	53	10	rectangles	rectangle	NOUN
ejpam-3605	53	11	aca1c1	aca1c1	NOUN
ejpam-3605	53	12	,	,	PUNCT
ejpam-3605	53	13	a1b1c1b	a1b1c1b	NOUN
ejpam-3605	53	14	,	,	PUNCT
ejpam-3605	53	15	abcc1	abcc1	NOUN
ejpam-3605	53	16	,	,	PUNCT
ejpam-3605	53	17	abca1	abca1	PROPN
ejpam-3605	53	18	,	,	PUNCT
ejpam-3605	53	19	respectively	respectively	ADV
ejpam-3605	53	20	,	,	PUNCT
ejpam-3605	53	21	we	we	PRON
ejpam-3605	53	22	obtain	obtain	VERB
ejpam-3605	53	23	aa1	aa1	PROPN
ejpam-3605	53	24	·	·	PUNCT
ejpam-3605	53	25	cc1	cc1	PROPN
ejpam-3605	53	26	=	=	PUNCT
ejpam-3605	53	27	ac	ac	PROPN
ejpam-3605	53	28	·	·	PUNCT
ejpam-3605	53	29	a1c1	a1c1	PRON
ejpam-3605	53	30	+	+	CCONJ
ejpam-3605	53	31	ac1	ac1	PROPN
ejpam-3605	53	32	·	·	PUNCT
ejpam-3605	53	33	ca1	ca1	PROPN
ejpam-3605	53	34	,	,	PUNCT
ejpam-3605	53	35	(	(	PUNCT
ejpam-3605	53	36	5	5	NUM
ejpam-3605	53	37	)	)	PUNCT
ejpam-3605	53	38	a1c1	a1c1	PRON
ejpam-3605	53	39	·	·	PUNCT
ejpam-3605	53	40	bb1	bb1	NOUN
ejpam-3605	53	41	=	=	SYM
ejpam-3605	53	42	ba1	ba1	PROPN
ejpam-3605	53	43	·	·	PUNCT
ejpam-3605	53	44	b1c1	b1c1	X
ejpam-3605	53	45	+	+	CCONJ
ejpam-3605	53	46	a1b1	a1b1	PROPN
ejpam-3605	53	47	·	·	SYM
ejpam-3605	53	48	bc1	bc1	NOUN
ejpam-3605	53	49	,	,	PUNCT
ejpam-3605	53	50	(	(	PUNCT
ejpam-3605	53	51	6	6	X
ejpam-3605	53	52	)	)	PUNCT
ejpam-3605	53	53	ac	ac	NOUN
ejpam-3605	53	54	·	·	PUNCT
ejpam-3605	53	55	bc1	bc1	NOUN
ejpam-3605	53	56	=	=	SYM
ejpam-3605	53	57	ab	ab	PROPN
ejpam-3605	53	58	·	·	PUNCT
ejpam-3605	53	59	cc1	cc1	PROPN
ejpam-3605	53	60	+	+	CCONJ
ejpam-3605	53	61	bc	bc	PROPN
ejpam-3605	53	62	·	·	PUNCT
ejpam-3605	53	63	ac1	ac1	PROPN
ejpam-3605	53	64	,	,	PUNCT
ejpam-3605	53	65	(	(	PUNCT
ejpam-3605	53	66	7	7	X
ejpam-3605	53	67	)	)	PUNCT
ejpam-3605	53	68	ac	ac	PROPN
ejpam-3605	53	69	·	·	PUNCT
ejpam-3605	53	70	ba1	ba1	PROPN
ejpam-3605	53	71	=	=	SYM
ejpam-3605	53	72	ab	ab	PROPN
ejpam-3605	53	73	·	·	PUNCT
ejpam-3605	53	74	ca1	ca1	PROPN
ejpam-3605	53	75	+	+	CCONJ
ejpam-3605	53	76	bc	bc	PROPN
ejpam-3605	53	77	·	·	PROPN
ejpam-3605	53	78	aa1	aa1	PROPN
ejpam-3605	53	79	.	.	PUNCT
ejpam-3605	54	1	(	(	PUNCT
ejpam-3605	54	2	8)	8)	NUM
ejpam-3605	54	3	then	then	ADV
ejpam-3605	54	4	,	,	PUNCT
ejpam-3605	54	5	multiplying	multiplying	NOUN
ejpam-3605	54	6	(	(	PUNCT
ejpam-3605	54	7	5	5	NUM
ejpam-3605	54	8	)	)	PUNCT
ejpam-3605	54	9	,	,	PUNCT
ejpam-3605	54	10	(	(	PUNCT
ejpam-3605	54	11	6	6	NUM
ejpam-3605	54	12	)	)	PUNCT
ejpam-3605	54	13	,	,	PUNCT
ejpam-3605	54	14	(	(	PUNCT
ejpam-3605	54	15	7	7	NUM
ejpam-3605	54	16	)	)	PUNCT
ejpam-3605	54	17	,	,	PUNCT
ejpam-3605	54	18	(	(	PUNCT
ejpam-3605	54	19	8)	8)	NUM
ejpam-3605	54	20	by	by	ADP
ejpam-3605	54	21	bb1	bb1	PROPN
ejpam-3605	54	22	,	,	PUNCT
ejpam-3605	54	23	ac	ac	PROPN
ejpam-3605	54	24	,	,	PUNCT
ejpam-3605	54	25	a1b1	a1b1	INTJ
ejpam-3605	54	26	,	,	PUNCT
ejpam-3605	54	27	b1c1	b1c1	NOUN
ejpam-3605	54	28	,	,	PUNCT
ejpam-3605	54	29	respectively	respectively	ADV
ejpam-3605	54	30	,	,	PUNCT
ejpam-3605	54	31	and	and	CCONJ
ejpam-3605	54	32	adding	add	VERB
ejpam-3605	54	33	up	up	ADP
ejpam-3605	54	34	the	the	DET
ejpam-3605	54	35	resulting	result	VERB
ejpam-3605	54	36	equalities	equality	NOUN
ejpam-3605	54	37	we	we	PRON
ejpam-3605	54	38	obtain	obtain	VERB
ejpam-3605	54	39	the	the	DET
ejpam-3605	54	40	relation	relation	NOUN
ejpam-3605	54	41	(	(	PUNCT
ejpam-3605	54	42	4	4	NUM
ejpam-3605	54	43	)	)	PUNCT
ejpam-3605	54	44	.	.	PUNCT
ejpam-3605	55	1	the	the	DET
ejpam-3605	55	2	equality	equality	NOUN
ejpam-3605	55	3	(	(	PUNCT
ejpam-3605	55	4	4	4	NUM
ejpam-3605	55	5	)	)	PUNCT
ejpam-3605	55	6	is	be	AUX
ejpam-3605	55	7	a	a	DET
ejpam-3605	55	8	relationship	relationship	NOUN
ejpam-3605	55	9	between	between	ADP
ejpam-3605	55	10	the	the	DET
ejpam-3605	55	11	sides	side	NOUN
ejpam-3605	55	12	and	and	CCONJ
ejpam-3605	55	13	diagonals	diagonal	NOUN
ejpam-3605	55	14	of	of	ADP
ejpam-3605	55	15	an	an	DET
ejpam-3605	55	16	inscribed	inscribe	VERB
ejpam-3605	55	17	hexagon	hexagon	NOUN
ejpam-3605	55	18	.	.	PUNCT
ejpam-3605	56	1	that	that	PRON
ejpam-3605	56	2	’s	’	VERB
ejpam-3605	56	3	why	why	SCONJ
ejpam-3605	56	4	it	it	PRON
ejpam-3605	56	5	can	can	AUX
ejpam-3605	56	6	well	well	ADV
ejpam-3605	56	7	be	be	AUX
ejpam-3605	56	8	called	call	VERB
ejpam-3605	56	9	an	an	DET
ejpam-3605	56	10	analogue	analogue	NOUN
ejpam-3605	56	11	of	of	ADP
ejpam-3605	56	12	ptolemy	ptolemy	PROPN
ejpam-3605	56	13	’s	’s	PART
ejpam-3605	56	14	theorem	theorem	NOUN
ejpam-3605	56	15	for	for	ADP
ejpam-3605	56	16	an	an	DET
ejpam-3605	56	17	inscribed	inscribe	VERB
ejpam-3605	56	18	hexagon	hexagon	NOUN
ejpam-3605	56	19	.	.	PUNCT
ejpam-3605	57	1	references	reference	NOUN
ejpam-3605	57	2	184	184	NUM
ejpam-3605	57	3	references	reference	NOUN
ejpam-3605	57	4	[	[	X
ejpam-3605	57	5	1	1	NUM
ejpam-3605	57	6	]	]	X
ejpam-3605	57	7	v.a	v.a	PROPN
ejpam-3605	57	8	.	.	PROPN
ejpam-3605	57	9	dalinger	dalinger	NOUN
ejpam-3605	57	10	;	;	PUNCT
ejpam-3605	57	11	graphics	graphic	NOUN
ejpam-3605	57	12	teaches	teach	VERB
ejpam-3605	57	13	how	how	SCONJ
ejpam-3605	57	14	to	to	PART
ejpam-3605	57	15	think	think	VERB
ejpam-3605	57	16	,	,	PUNCT
ejpam-3605	57	17	matematika	matematika	PROPN
ejpam-3605	57	18	v	v	PROPN
ejpam-3605	57	19	shkole	shkole	NOUN
ejpam-3605	57	20	,	,	PUNCT
ejpam-3605	57	21	(	(	PUNCT
ejpam-3605	57	22	1990	1990	NUM
ejpam-3605	57	23	)	)	PUNCT
ejpam-3605	57	24	,	,	PUNCT
ejpam-3605	57	25	no4	no4	X
ejpam-3605	57	26	,	,	PUNCT
ejpam-3605	57	27	p.32	p.32	VERB
ejpam-3605	57	28	-	-	SYM
ejpam-3605	57	29	36	36	NUM
ejpam-3605	57	30	.	.	PUNCT
ejpam-3605	58	1	(	(	PUNCT
ejpam-3605	58	2	in	in	ADP
ejpam-3605	58	3	russian	russian	NOUN
ejpam-3605	58	4	)	)	PUNCT
ejpam-3605	59	1	[	[	X
ejpam-3605	59	2	2	2	NUM
ejpam-3605	59	3	]	]	PUNCT
ejpam-3605	59	4	v.y.kutsenok	v.y.kutsenok	NOUN
ejpam-3605	59	5	;	;	PUNCT
ejpam-3605	59	6	the	the	DET
ejpam-3605	59	7	circle	circle	NOUN
ejpam-3605	59	8	helps	help	VERB
ejpam-3605	59	9	to	to	PART
ejpam-3605	59	10	solve	solve	VERB
ejpam-3605	59	11	problems	problem	NOUN
ejpam-3605	59	12	,	,	PUNCT
ejpam-3605	59	13	matematika	matematika	PROPN
ejpam-3605	59	14	v	v	ADP
ejpam-3605	59	15	shkole,(1990	shkole,(1990	NOUN
ejpam-3605	59	16	)	)	PUNCT
ejpam-3605	59	17	,	,	PUNCT
ejpam-3605	59	18	no2	no2	NOUN
ejpam-3605	59	19	,	,	PUNCT
ejpam-3605	59	20	p.55	p.55	NOUN
ejpam-3605	59	21	-	-	NOUN
ejpam-3605	59	22	30	30	NUM
ejpam-3605	59	23	.	.	PUNCT
ejpam-3605	60	1	(	(	PUNCT
ejpam-3605	60	2	in	in	ADP
ejpam-3605	60	3	russian	russian	NOUN
ejpam-3605	60	4	)	)	PUNCT
ejpam-3605	61	1	[	[	X
ejpam-3605	61	2	3	3	NUM
ejpam-3605	61	3	]	]	PUNCT
ejpam-3605	61	4	v.y.kutsenok	v.y.kutsenok	NOUN
ejpam-3605	61	5	;	;	PUNCT
ejpam-3605	61	6	teaching	teach	VERB
ejpam-3605	61	7	the	the	DET
ejpam-3605	61	8	methods	method	NOUN
ejpam-3605	61	9	of	of	ADP
ejpam-3605	61	10	solving	solve	VERB
ejpam-3605	61	11	geometric	geometric	ADJ
ejpam-3605	61	12	problems	problem	NOUN
ejpam-3605	61	13	based	base	VERB
ejpam-3605	61	14	on	on	ADP
ejpam-3605	61	15	the	the	DET
ejpam-3605	61	16	use	use	NOUN
ejpam-3605	61	17	of	of	ADP
ejpam-3605	61	18	auxiliary	auxiliary	ADJ
ejpam-3605	61	19	circle	circle	NOUN
ejpam-3605	61	20	,	,	PUNCT
ejpam-3605	61	21	phd	phd	NOUN
ejpam-3605	61	22	thesis	thesis	NOUN
ejpam-3605	61	23	in	in	ADP
ejpam-3605	61	24	pedagogics	pedagogic	NOUN
ejpam-3605	61	25	,	,	PUNCT
ejpam-3605	61	26	moscow	moscow	PROPN
ejpam-3605	61	27	,	,	PUNCT
ejpam-3605	61	28	(	(	PUNCT
ejpam-3605	61	29	1992).(in	1992).(in	NUM
ejpam-3605	61	30	russian	russian	NOUN
ejpam-3605	61	31	)	)	PUNCT
ejpam-3605	62	1	[	[	X
ejpam-3605	62	2	4	4	NUM
ejpam-3605	62	3	]	]	PUNCT
ejpam-3605	62	4	y.p.ponarin	y.p.ponarin	NOUN
ejpam-3605	62	5	;	;	PUNCT
ejpam-3605	62	6	elementary	elementary	ADJ
ejpam-3605	62	7	geometry	geometry	NOUN
ejpam-3605	62	8	,	,	PUNCT
ejpam-3605	62	9	v.1	v.1	NUM
ejpam-3605	62	10	.	.	PUNCT
ejpam-3605	63	1	moscow	moscow	PROPN
ejpam-3605	63	2	,	,	PUNCT
ejpam-3605	63	3	mtsnmo	mtsnmo	NOUN
ejpam-3605	63	4	,	,	PUNCT
ejpam-3605	63	5	(	(	PUNCT
ejpam-3605	63	6	2008	2008	NUM
ejpam-3605	63	7	)	)	PUNCT
ejpam-3605	63	8	,	,	PUNCT
ejpam-3605	63	9	312	312	NUM
ejpam-3605	63	10	p.	p.	NOUN
ejpam-3605	63	11	(	(	PUNCT
ejpam-3605	63	12	in	in	ADP
ejpam-3605	63	13	russian	russian	NOUN
ejpam-3605	63	14	)	)	PUNCT
ejpam-3605	64	1	[	[	X
ejpam-3605	64	2	5	5	NUM
ejpam-3605	64	3	]	]	PUNCT
ejpam-3605	64	4	i.f.sharigin	i.f.sharigin	NOUN
ejpam-3605	64	5	;	;	PUNCT
ejpam-3605	64	6	geometry	geometry	NOUN
ejpam-3605	64	7	,	,	PUNCT
ejpam-3605	64	8	m.	m.	NOUN
ejpam-3605	64	9	:	:	PUNCT
ejpam-3605	64	10	drofa	drofa	NOUN
ejpam-3605	64	11	,	,	PUNCT
ejpam-3605	64	12	(	(	PUNCT
ejpam-3605	64	13	1999	1999	NUM
ejpam-3605	64	14	)	)	PUNCT
ejpam-3605	64	15	,	,	PUNCT
ejpam-3605	64	16	352	352	NUM
ejpam-3605	64	17	p.	p.	NOUN
ejpam-3605	64	18	(	(	PUNCT
ejpam-3605	64	19	in	in	ADP
ejpam-3605	64	20	russian	russian	NOUN
ejpam-3605	64	21	)	)	PUNCT