id	sid	tid	token	lemma	pos
ejpam-4721	1	1	european	european	PROPN
ejpam-4721	1	2	journal	journal	PROPN
ejpam-4721	1	3	of	of	ADP
ejpam-4721	1	4	pure	pure	ADJ
ejpam-4721	1	5	and	and	CCONJ
ejpam-4721	1	6	applied	apply	VERB
ejpam-4721	1	7	mathematics	mathematic	NOUN
ejpam-4721	1	8	vol	vol	NOUN
ejpam-4721	1	9	.	.	PUNCT
ejpam-4721	2	1	16	16	NUM
ejpam-4721	2	2	,	,	PUNCT
ejpam-4721	2	3	no	no	INTJ
ejpam-4721	2	4	.	.	NOUN
ejpam-4721	2	5	2	2	NUM
ejpam-4721	2	6	,	,	PUNCT
ejpam-4721	2	7	2023	2023	NUM
ejpam-4721	2	8	,	,	PUNCT
ejpam-4721	2	9	1110	1110	NUM
ejpam-4721	2	10	-	-	SYM
ejpam-4721	2	11	1117	1117	NUM
ejpam-4721	3	1	issn	issn	PROPN
ejpam-4721	3	2	1307	1307	NUM
ejpam-4721	3	3	-	-	SYM
ejpam-4721	3	4	5543	5543	NUM
ejpam-4721	3	5	–	–	PUNCT
ejpam-4721	3	6	ejpam.com	ejpam.com	X
ejpam-4721	3	7	published	publish	VERB
ejpam-4721	3	8	by	by	ADP
ejpam-4721	3	9	new	new	PROPN
ejpam-4721	3	10	york	york	PROPN
ejpam-4721	3	11	business	business	PROPN
ejpam-4721	3	12	global	global	ADJ
ejpam-4721	3	13	solving	solving	NOUN
ejpam-4721	3	14	geometry	geometry	NOUN
ejpam-4721	3	15	problems	problem	NOUN
ejpam-4721	3	16	by	by	ADP
ejpam-4721	3	17	alternative	alternative	ADJ
ejpam-4721	3	18	methods	method	NOUN
ejpam-4721	3	19	in	in	ADP
ejpam-4721	3	20	mathematics	mathematics	NOUN
ejpam-4721	3	21	education	education	NOUN
ejpam-4721	3	22	samed	samed	PROPN
ejpam-4721	3	23	j.aliyev1,∗	j.aliyev1,∗	NOUN
ejpam-4721	3	24	,	,	PUNCT
ejpam-4721	3	25	maftun	maftun	PROPN
ejpam-4721	3	26	n.heydarova2	n.heydarova2	PROPN
ejpam-4721	3	27	,	,	PUNCT
ejpam-4721	3	28	shahin	shahin	NOUN
ejpam-4721	3	29	m.aghazade1	m.aghazade1	NOUN
ejpam-4721	3	30	1	1	NUM
ejpam-4721	3	31	department	department	NOUN
ejpam-4721	3	32	of	of	ADP
ejpam-4721	3	33	methods	method	NOUN
ejpam-4721	3	34	of	of	ADP
ejpam-4721	3	35	mathematics	mathematic	NOUN
ejpam-4721	3	36	and	and	CCONJ
ejpam-4721	3	37	its	its	PRON
ejpam-4721	3	38	teaching	teaching	NOUN
ejpam-4721	3	39	,	,	PUNCT
ejpam-4721	3	40	faculty	faculty	NOUN
ejpam-4721	3	41	of	of	ADP
ejpam-4721	3	42	mechanics	mechanic	NOUN
ejpam-4721	3	43	and	and	CCONJ
ejpam-4721	3	44	mathematics	mathematic	NOUN
ejpam-4721	3	45	,	,	PUNCT
ejpam-4721	3	46	baku	baku	PROPN
ejpam-4721	3	47	state	state	PROPN
ejpam-4721	3	48	university	university	PROPN
ejpam-4721	3	49	,	,	PUNCT
ejpam-4721	3	50	baku	baku	PROPN
ejpam-4721	3	51	,	,	PUNCT
ejpam-4721	3	52	z.khalilov	z.khalilov	PROPN
ejpam-4721	3	53	str	str	NOUN
ejpam-4721	3	54	.	.	PROPN
ejpam-4721	3	55	23	23	NUM
ejpam-4721	3	56	,	,	PUNCT
ejpam-4721	3	57	az	az	PROPN
ejpam-4721	3	58	1148	1148	NUM
ejpam-4721	3	59	,	,	PUNCT
ejpam-4721	3	60	azerbaijan	azerbaijan	PROPN
ejpam-4721	3	61	2	2	NUM
ejpam-4721	3	62	department	department	NOUN
ejpam-4721	3	63	of	of	ADP
ejpam-4721	3	64	methods	method	NOUN
ejpam-4721	3	65	of	of	ADP
ejpam-4721	3	66	mathematics	mathematic	NOUN
ejpam-4721	3	67	and	and	CCONJ
ejpam-4721	3	68	its	its	PRON
ejpam-4721	3	69	teaching	teaching	NOUN
ejpam-4721	3	70	,	,	PUNCT
ejpam-4721	3	71	faculty	faculty	NOUN
ejpam-4721	3	72	of	of	ADP
ejpam-4721	3	73	mathematics	mathematic	NOUN
ejpam-4721	3	74	,	,	PUNCT
ejpam-4721	3	75	sumgait	sumgait	VERB
ejpam-4721	3	76	state	state	PROPN
ejpam-4721	3	77	university	university	PROPN
ejpam-4721	3	78	,	,	PUNCT
ejpam-4721	3	79	sumgait	sumgait	NOUN
ejpam-4721	3	80	,	,	PUNCT
ejpam-4721	3	81	district	district	NOUN
ejpam-4721	3	82	43	43	NUM
ejpam-4721	3	83	,	,	PUNCT
ejpam-4721	3	84	az	az	PROPN
ejpam-4721	3	85	5008	5008	NUM
ejpam-4721	3	86	,	,	PUNCT
ejpam-4721	3	87	azerbaijan	azerbaijan	PROPN
ejpam-4721	3	88	abstract	abstract	NOUN
ejpam-4721	3	89	.	.	PUNCT
ejpam-4721	4	1	solving	solve	VERB
ejpam-4721	4	2	geometry	geometry	NOUN
ejpam-4721	4	3	problems	problem	NOUN
ejpam-4721	4	4	is	be	AUX
ejpam-4721	4	5	both	both	PRON
ejpam-4721	4	6	difficult	difficult	ADJ
ejpam-4721	4	7	and	and	CCONJ
ejpam-4721	4	8	interesting	interesting	ADJ
ejpam-4721	4	9	.	.	PUNCT
ejpam-4721	4	10	difficult	difficult	ADJ
ejpam-4721	4	11	because	because	SCONJ
ejpam-4721	4	12	there	there	PRON
ejpam-4721	4	13	is	be	VERB
ejpam-4721	4	14	no	no	DET
ejpam-4721	4	15	general	general	ADJ
ejpam-4721	4	16	algorithm	algorithm	NOUN
ejpam-4721	4	17	to	to	PART
ejpam-4721	4	18	solve	solve	VERB
ejpam-4721	4	19	more	more	ADJ
ejpam-4721	4	20	or	or	CCONJ
ejpam-4721	4	21	less	less	ADJ
ejpam-4721	4	22	non	non	ADJ
ejpam-4721	4	23	-	-	ADJ
ejpam-4721	4	24	trivial	trivial	ADJ
ejpam-4721	4	25	problems	problem	NOUN
ejpam-4721	4	26	as	as	SCONJ
ejpam-4721	4	27	every	every	DET
ejpam-4721	4	28	single	single	ADJ
ejpam-4721	4	29	problem	problem	NOUN
ejpam-4721	4	30	requires	require	VERB
ejpam-4721	4	31	individual	individual	ADJ
ejpam-4721	4	32	and	and	CCONJ
ejpam-4721	4	33	creative	creative	ADJ
ejpam-4721	4	34	approach	approach	NOUN
ejpam-4721	4	35	.	.	PUNCT
ejpam-4721	5	1	at	at	ADP
ejpam-4721	5	2	the	the	DET
ejpam-4721	5	3	same	same	ADJ
ejpam-4721	5	4	time	time	NOUN
ejpam-4721	5	5	,	,	PUNCT
ejpam-4721	5	6	this	this	PRON
ejpam-4721	5	7	is	be	AUX
ejpam-4721	5	8	a	a	DET
ejpam-4721	5	9	very	very	ADV
ejpam-4721	5	10	interesting	interesting	ADJ
ejpam-4721	5	11	activity	activity	NOUN
ejpam-4721	5	12	,	,	PUNCT
ejpam-4721	5	13	because	because	SCONJ
ejpam-4721	5	14	for	for	ADP
ejpam-4721	5	15	almost	almost	ADV
ejpam-4721	5	16	every	every	PRON
ejpam-4721	5	17	problem	problem	NOUN
ejpam-4721	5	18	there	there	PRON
ejpam-4721	5	19	are	be	VERB
ejpam-4721	5	20	plenty	plenty	NOUN
ejpam-4721	5	21	of	of	ADP
ejpam-4721	5	22	ways	way	NOUN
ejpam-4721	5	23	to	to	PART
ejpam-4721	5	24	solve	solve	VERB
ejpam-4721	5	25	it	it	PRON
ejpam-4721	5	26	.	.	PUNCT
ejpam-4721	6	1	in	in	ADP
ejpam-4721	6	2	this	this	DET
ejpam-4721	6	3	work	work	NOUN
ejpam-4721	6	4	,	,	PUNCT
ejpam-4721	6	5	we	we	PRON
ejpam-4721	6	6	present	present	VERB
ejpam-4721	6	7	the	the	DET
ejpam-4721	6	8	method	method	NOUN
ejpam-4721	6	9	of	of	ADP
ejpam-4721	6	10	auxiliary	auxiliary	ADJ
ejpam-4721	6	11	circle	circle	NOUN
ejpam-4721	6	12	divided	divide	VERB
ejpam-4721	6	13	into	into	ADP
ejpam-4721	6	14	equal	equal	ADJ
ejpam-4721	6	15	parts	part	NOUN
ejpam-4721	6	16	.	.	PUNCT
ejpam-4721	7	1	this	this	DET
ejpam-4721	7	2	method	method	NOUN
ejpam-4721	7	3	allows	allow	VERB
ejpam-4721	7	4	finding	find	VERB
ejpam-4721	7	5	solution	solution	NOUN
ejpam-4721	7	6	algorithm	algorithm	NOUN
ejpam-4721	7	7	for	for	ADP
ejpam-4721	7	8	some	some	DET
ejpam-4721	7	9	geometry	geometry	NOUN
ejpam-4721	7	10	problems	problem	NOUN
ejpam-4721	7	11	which	which	PRON
ejpam-4721	7	12	are	be	AUX
ejpam-4721	7	13	hard	hard	ADJ
ejpam-4721	7	14	to	to	PART
ejpam-4721	7	15	solve	solve	VERB
ejpam-4721	7	16	by	by	ADP
ejpam-4721	7	17	the	the	DET
ejpam-4721	7	18	method	method	NOUN
ejpam-4721	7	19	of	of	ADP
ejpam-4721	7	20	additional	additional	ADJ
ejpam-4721	7	21	constructions	construction	NOUN
ejpam-4721	7	22	.	.	PUNCT
ejpam-4721	8	1	2020	2020	NUM
ejpam-4721	8	2	mathematics	mathematic	NOUN
ejpam-4721	8	3	subject	subject	NOUN
ejpam-4721	8	4	classifications	classification	NOUN
ejpam-4721	8	5	:	:	PUNCT
ejpam-4721	8	6	97g10	97g10	NUM
ejpam-4721	8	7	,	,	PUNCT
ejpam-4721	8	8	97g30	97g30	NUM
ejpam-4721	8	9	,	,	PUNCT
ejpam-4721	8	10	97g40	97g40	NUM
ejpam-4721	8	11	key	key	ADJ
ejpam-4721	8	12	words	word	NOUN
ejpam-4721	8	13	and	and	CCONJ
ejpam-4721	8	14	phrases	phrase	NOUN
ejpam-4721	8	15	:	:	PUNCT
ejpam-4721	8	16	geometry	geometry	NOUN
ejpam-4721	8	17	problem	problem	NOUN
ejpam-4721	8	18	,	,	PUNCT
ejpam-4721	8	19	ceva	ceva	PROPN
ejpam-4721	8	20	’s	’s	PART
ejpam-4721	8	21	theorem	theorem	ADJ
ejpam-4721	8	22	,	,	PUNCT
ejpam-4721	8	23	regular	regular	ADJ
ejpam-4721	8	24	polygon	polygon	NOUN
ejpam-4721	8	25	,	,	PUNCT
ejpam-4721	8	26	solution	solution	NOUN
ejpam-4721	8	27	algorithm	algorithm	NOUN
ejpam-4721	8	28	.	.	PUNCT
ejpam-4721	9	1	1	1	X
ejpam-4721	9	2	.	.	X
ejpam-4721	9	3	introduction	introduction	NOUN
ejpam-4721	9	4	in	in	ADP
ejpam-4721	9	5	geometry	geometry	NOUN
ejpam-4721	9	6	,	,	PUNCT
ejpam-4721	9	7	there	there	PRON
ejpam-4721	9	8	is	be	VERB
ejpam-4721	9	9	a	a	DET
ejpam-4721	9	10	class	class	NOUN
ejpam-4721	9	11	of	of	ADP
ejpam-4721	9	12	problems	problem	NOUN
ejpam-4721	9	13	for	for	ADP
ejpam-4721	9	14	which	which	PRON
ejpam-4721	9	15	the	the	DET
ejpam-4721	9	16	traditional	traditional	ADJ
ejpam-4721	9	17	methods	method	NOUN
ejpam-4721	9	18	(	(	PUNCT
ejpam-4721	9	19	such	such	ADJ
ejpam-4721	9	20	as	as	ADP
ejpam-4721	9	21	the	the	DET
ejpam-4721	9	22	method	method	NOUN
ejpam-4721	9	23	of	of	ADP
ejpam-4721	9	24	equal	equal	ADJ
ejpam-4721	9	25	triangles	triangle	NOUN
ejpam-4721	9	26	,	,	PUNCT
ejpam-4721	9	27	the	the	DET
ejpam-4721	9	28	method	method	NOUN
ejpam-4721	9	29	of	of	ADP
ejpam-4721	9	30	geometric	geometric	ADJ
ejpam-4721	9	31	transformations	transformation	NOUN
ejpam-4721	9	32	,	,	PUNCT
ejpam-4721	9	33	the	the	DET
ejpam-4721	9	34	vector	vector	NOUN
ejpam-4721	9	35	method	method	NOUN
ejpam-4721	9	36	,	,	PUNCT
ejpam-4721	9	37	etc	etc	X
ejpam-4721	9	38	.	.	X
ejpam-4721	9	39	)	)	PUNCT
ejpam-4721	9	40	are	be	AUX
ejpam-4721	9	41	either	either	CCONJ
ejpam-4721	9	42	inapplicable	inapplicable	ADJ
ejpam-4721	9	43	or	or	CCONJ
ejpam-4721	9	44	provide	provide	VERB
ejpam-4721	9	45	complicated	complicated	ADJ
ejpam-4721	9	46	and	and	CCONJ
ejpam-4721	9	47	cumber	cumber	NOUN
ejpam-4721	9	48	-	-	PUNCT
ejpam-4721	9	49	some	some	PRON
ejpam-4721	9	50	solutions	solution	NOUN
ejpam-4721	9	51	.	.	PUNCT
ejpam-4721	10	1	in	in	ADP
ejpam-4721	10	2	many	many	ADJ
ejpam-4721	10	3	cases	case	NOUN
ejpam-4721	10	4	,	,	PUNCT
ejpam-4721	10	5	it	it	PRON
ejpam-4721	10	6	becomes	become	VERB
ejpam-4721	10	7	possible	possible	ADJ
ejpam-4721	10	8	to	to	PART
ejpam-4721	10	9	solve	solve	VERB
ejpam-4721	10	10	such	such	ADJ
ejpam-4721	10	11	kind	kind	NOUN
ejpam-4721	10	12	of	of	ADP
ejpam-4721	10	13	problems	problem	NOUN
ejpam-4721	10	14	by	by	ADP
ejpam-4721	10	15	adding	add	VERB
ejpam-4721	10	16	some	some	DET
ejpam-4721	10	17	lines	line	NOUN
ejpam-4721	10	18	(	(	PUNCT
ejpam-4721	10	19	so	so	ADV
ejpam-4721	10	20	called	call	VERB
ejpam-4721	10	21	additional	additional	ADJ
ejpam-4721	10	22	constructions	construction	NOUN
ejpam-4721	10	23	)	)	PUNCT
ejpam-4721	10	24	to	to	ADP
ejpam-4721	10	25	the	the	DET
ejpam-4721	10	26	drawing	drawing	NOUN
ejpam-4721	10	27	.	.	PUNCT
ejpam-4721	11	1	sometimes	sometimes	ADV
ejpam-4721	11	2	these	these	DET
ejpam-4721	11	3	constructions	construction	NOUN
ejpam-4721	11	4	suggest	suggest	VERB
ejpam-4721	11	5	themselves	themselves	PRON
ejpam-4721	11	6	,	,	PUNCT
ejpam-4721	11	7	but	but	CCONJ
ejpam-4721	11	8	in	in	ADP
ejpam-4721	11	9	other	other	ADJ
ejpam-4721	11	10	cases	case	NOUN
ejpam-4721	11	11	situation	situation	NOUN
ejpam-4721	11	12	may	may	AUX
ejpam-4721	11	13	depend	depend	VERB
ejpam-4721	11	14	on	on	ADP
ejpam-4721	11	15	your	your	PRON
ejpam-4721	11	16	experience	experience	NOUN
ejpam-4721	11	17	,	,	PUNCT
ejpam-4721	11	18	expertise	expertise	NOUN
ejpam-4721	11	19	and	and	CCONJ
ejpam-4721	11	20	geometric	geometric	ADJ
ejpam-4721	11	21	intuition	intuition	NOUN
ejpam-4721	11	22	.	.	PUNCT
ejpam-4721	12	1	the	the	DET
ejpam-4721	12	2	method	method	NOUN
ejpam-4721	12	3	of	of	ADP
ejpam-4721	12	4	solving	solve	VERB
ejpam-4721	12	5	problems	problem	NOUN
ejpam-4721	12	6	by	by	ADP
ejpam-4721	12	7	adding	add	VERB
ejpam-4721	12	8	some	some	DET
ejpam-4721	12	9	constructions	construction	NOUN
ejpam-4721	12	10	to	to	ADP
ejpam-4721	12	11	the	the	DET
ejpam-4721	12	12	drawing	drawing	NOUN
ejpam-4721	12	13	is	be	AUX
ejpam-4721	12	14	called	call	VERB
ejpam-4721	12	15	the	the	DET
ejpam-4721	12	16	method	method	NOUN
ejpam-4721	12	17	of	of	ADP
ejpam-4721	12	18	additional	additional	ADJ
ejpam-4721	12	19	constructions	construction	NOUN
ejpam-4721	12	20	.	.	PUNCT
ejpam-4721	13	1	the	the	DET
ejpam-4721	13	2	essence	essence	NOUN
ejpam-4721	13	3	of	of	ADP
ejpam-4721	13	4	the	the	DET
ejpam-4721	13	5	method	method	NOUN
ejpam-4721	13	6	of	of	ADP
ejpam-4721	13	7	additional	additional	ADJ
ejpam-4721	13	8	constructions	construction	NOUN
ejpam-4721	13	9	lies	lie	VERB
ejpam-4721	13	10	in	in	ADP
ejpam-4721	13	11	the	the	DET
ejpam-4721	13	12	fact	fact	NOUN
ejpam-4721	13	13	that	that	SCONJ
ejpam-4721	13	14	you	you	PRON
ejpam-4721	13	15	add	add	VERB
ejpam-4721	13	16	some	some	DET
ejpam-4721	13	17	new	new	ADJ
ejpam-4721	13	18	(	(	PUNCT
ejpam-4721	13	19	auxiliary	auxiliary	ADJ
ejpam-4721	13	20	)	)	PUNCT
ejpam-4721	13	21	elements	element	NOUN
ejpam-4721	13	22	to	to	ADP
ejpam-4721	13	23	the	the	DET
ejpam-4721	13	24	drawing	drawing	NOUN
ejpam-4721	13	25	of	of	ADP
ejpam-4721	13	26	∗corresponding	∗corresponde	VERB
ejpam-4721	13	27	author	author	NOUN
ejpam-4721	13	28	.	.	PUNCT
ejpam-4721	14	1	doi	doi	NOUN
ejpam-4721	14	2	:	:	PUNCT
ejpam-4721	14	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4721	https://doi.org/10.29020/nybg.ejpam.v16i2.4721	PROPN
ejpam-4721	14	4	email	email	NOUN
ejpam-4721	14	5	addresses	address	NOUN
ejpam-4721	14	6	:	:	PUNCT
ejpam-4721	14	7	samed59@bk.ru	samed59@bk.ru	PROPN
ejpam-4721	14	8	(	(	PUNCT
ejpam-4721	14	9	s	s	X
ejpam-4721	14	10	,	,	PUNCT
ejpam-4721	14	11	j.aliyev	j.aliyev	ADJ
ejpam-4721	14	12	)	)	PUNCT
ejpam-4721	14	13	,	,	PUNCT
ejpam-4721	14	14	meftun.heydarova.82@mail.ru	meftun.heydarova.82@mail.ru	PROPN
ejpam-4721	14	15	(	(	PUNCT
ejpam-4721	14	16	m.n.heydarova),shahinaghazade@bsu.edu.az	m.n.heydarova),shahinaghazade@bsu.edu.az	X
ejpam-4721	14	17	(	(	PUNCT
ejpam-4721	14	18	sh.m.aghazade	sh.m.aghazade	PROPN
ejpam-4721	14	19	)	)	PUNCT
ejpam-4721	14	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4721	14	21	1110	1110	NUM
ejpam-4721	15	1	©	©	PROPN
ejpam-4721	15	2	2023	2023	NUM
ejpam-4721	15	3	ejpam	ejpam	NOUN
ejpam-4721	15	4	all	all	DET
ejpam-4721	15	5	rights	right	NOUN
ejpam-4721	15	6	reserved	reserve	VERB
ejpam-4721	15	7	.	.	PUNCT
ejpam-4721	16	1	s.	s.	PROPN
ejpam-4721	16	2	j.aliyev	j.aliyev	PROPN
ejpam-4721	16	3	,	,	PUNCT
ejpam-4721	16	4	m.	m.	PROPN
ejpam-4721	16	5	n.heydarova	n.heydarova	PROPN
ejpam-4721	16	6	,	,	PUNCT
ejpam-4721	16	7	s.	s.	PROPN
ejpam-4721	16	8	m.aghazade	m.aghazade	PROPN
ejpam-4721	16	9	/	/	SYM
ejpam-4721	16	10	eur	eur	PROPN
ejpam-4721	16	11	.	.	PUNCT
ejpam-4721	17	1	j.	j.	PROPN
ejpam-4721	17	2	pure	pure	PROPN
ejpam-4721	17	3	appl	appl	PROPN
ejpam-4721	17	4	.	.	PROPN
ejpam-4721	17	5	math	math	PROPN
ejpam-4721	17	6	,	,	PUNCT
ejpam-4721	17	7	16	16	NUM
ejpam-4721	17	8	(	(	PUNCT
ejpam-4721	17	9	2	2	NUM
ejpam-4721	17	10	)	)	PUNCT
ejpam-4721	17	11	(	(	PUNCT
ejpam-4721	17	12	2023	2023	NUM
ejpam-4721	17	13	)	)	PUNCT
ejpam-4721	17	14	,	,	PUNCT
ejpam-4721	17	15	1110	1110	NUM
ejpam-4721	17	16	-	-	SYM
ejpam-4721	17	17	1117	1117	NUM
ejpam-4721	17	18	1111	1111	NUM
ejpam-4721	17	19	figure	figure	NOUN
ejpam-4721	17	20	1	1	NUM
ejpam-4721	17	21	:	:	PUNCT
ejpam-4721	17	22	(	(	PUNCT
ejpam-4721	17	23	triangle	triangle	VERB
ejpam-4721	17	24	abc	abc	PROPN
ejpam-4721	17	25	with	with	ADP
ejpam-4721	17	26	the	the	DET
ejpam-4721	17	27	given	give	VERB
ejpam-4721	17	28	angles	angle	NOUN
ejpam-4721	17	29	)	)	PUNCT
ejpam-4721	17	30	your	your	PRON
ejpam-4721	17	31	problem	problem	NOUN
ejpam-4721	17	32	.	.	PUNCT
ejpam-4721	18	1	as	as	ADP
ejpam-4721	18	2	a	a	DET
ejpam-4721	18	3	result	result	NOUN
ejpam-4721	18	4	,	,	PUNCT
ejpam-4721	18	5	the	the	DET
ejpam-4721	18	6	relationships	relationship	NOUN
ejpam-4721	18	7	between	between	ADP
ejpam-4721	18	8	the	the	DET
ejpam-4721	18	9	problem	problem	NOUN
ejpam-4721	18	10	data	datum	NOUN
ejpam-4721	18	11	and	and	CCONJ
ejpam-4721	18	12	the	the	DET
ejpam-4721	18	13	unknown	unknown	ADJ
ejpam-4721	18	14	quantities	quantity	NOUN
ejpam-4721	18	15	,	,	PUNCT
ejpam-4721	18	16	which	which	PRON
ejpam-4721	18	17	have	have	AUX
ejpam-4721	18	18	been	be	AUX
ejpam-4721	18	19	hard	hard	ADJ
ejpam-4721	18	20	to	to	PART
ejpam-4721	18	21	see	see	VERB
ejpam-4721	18	22	before	before	ADV
ejpam-4721	18	23	,	,	PUNCT
ejpam-4721	18	24	become	become	VERB
ejpam-4721	18	25	more	more	ADV
ejpam-4721	18	26	tangible	tangible	ADJ
ejpam-4721	18	27	,	,	PUNCT
ejpam-4721	18	28	or	or	CCONJ
ejpam-4721	18	29	even	even	ADV
ejpam-4721	18	30	obvious	obvious	ADJ
ejpam-4721	18	31	.	.	PUNCT
ejpam-4721	19	1	there	there	PRON
ejpam-4721	19	2	are	be	VERB
ejpam-4721	19	3	problems	problem	NOUN
ejpam-4721	19	4	where	where	SCONJ
ejpam-4721	19	5	additional	additional	ADJ
ejpam-4721	19	6	constructions	construction	NOUN
ejpam-4721	19	7	are	be	AUX
ejpam-4721	19	8	the	the	DET
ejpam-4721	19	9	only	only	ADJ
ejpam-4721	19	10	way	way	NOUN
ejpam-4721	19	11	of	of	ADP
ejpam-4721	19	12	solution	solution	NOUN
ejpam-4721	19	13	.	.	PUNCT
ejpam-4721	20	1	solving	solve	VERB
ejpam-4721	20	2	geometry	geometry	NOUN
ejpam-4721	20	3	problems	problem	NOUN
ejpam-4721	20	4	by	by	ADP
ejpam-4721	20	5	the	the	DET
ejpam-4721	20	6	method	method	NOUN
ejpam-4721	20	7	of	of	ADP
ejpam-4721	20	8	additional	additional	ADJ
ejpam-4721	20	9	constructions	construction	NOUN
ejpam-4721	20	10	is	be	AUX
ejpam-4721	20	11	a	a	DET
ejpam-4721	20	12	very	very	ADV
ejpam-4721	20	13	hard	hard	ADJ
ejpam-4721	20	14	task	task	NOUN
ejpam-4721	20	15	,	,	PUNCT
ejpam-4721	20	16	because	because	SCONJ
ejpam-4721	20	17	there	there	PRON
ejpam-4721	20	18	is	be	VERB
ejpam-4721	20	19	no	no	DET
ejpam-4721	20	20	general	general	ADJ
ejpam-4721	20	21	algorithm	algorithm	NOUN
ejpam-4721	20	22	to	to	PART
ejpam-4721	20	23	solve	solve	VERB
ejpam-4721	20	24	your	your	PRON
ejpam-4721	20	25	problem	problem	NOUN
ejpam-4721	20	26	by	by	ADP
ejpam-4721	20	27	this	this	DET
ejpam-4721	20	28	method	method	NOUN
ejpam-4721	20	29	.	.	PUNCT
ejpam-4721	21	1	even	even	ADV
ejpam-4721	21	2	the	the	DET
ejpam-4721	21	3	schoolchildren	schoolchildren	NOUN
ejpam-4721	21	4	with	with	ADP
ejpam-4721	21	5	a	a	DET
ejpam-4721	21	6	good	good	ADJ
ejpam-4721	21	7	knowledge	knowledge	NOUN
ejpam-4721	21	8	of	of	ADP
ejpam-4721	21	9	geometry	geometry	NOUN
ejpam-4721	21	10	are	be	AUX
ejpam-4721	21	11	not	not	PART
ejpam-4721	21	12	able	able	ADJ
ejpam-4721	21	13	to	to	PART
ejpam-4721	21	14	solve	solve	VERB
ejpam-4721	21	15	such	such	ADJ
ejpam-4721	21	16	kind	kind	NOUN
ejpam-4721	21	17	of	of	ADP
ejpam-4721	21	18	problems	problem	NOUN
ejpam-4721	21	19	.	.	PUNCT
ejpam-4721	22	1	in	in	ADP
ejpam-4721	22	2	this	this	DET
ejpam-4721	22	3	work	work	NOUN
ejpam-4721	22	4	,	,	PUNCT
ejpam-4721	22	5	we	we	PRON
ejpam-4721	22	6	overcome	overcome	VERB
ejpam-4721	22	7	the	the	DET
ejpam-4721	22	8	above	above	ADV
ejpam-4721	22	9	mentioned	mention	VERB
ejpam-4721	22	10	difficulties	difficulty	NOUN
ejpam-4721	22	11	by	by	ADP
ejpam-4721	22	12	using	use	VERB
ejpam-4721	22	13	the	the	DET
ejpam-4721	22	14	method	method	NOUN
ejpam-4721	22	15	of	of	ADP
ejpam-4721	22	16	auxiliary	auxiliary	ADJ
ejpam-4721	22	17	circle	circle	NOUN
ejpam-4721	22	18	divided	divide	VERB
ejpam-4721	22	19	into	into	ADP
ejpam-4721	22	20	equal	equal	ADJ
ejpam-4721	22	21	parts	part	NOUN
ejpam-4721	22	22	.	.	PUNCT
ejpam-4721	23	1	namely	namely	ADV
ejpam-4721	23	2	,	,	PUNCT
ejpam-4721	23	3	we	we	PRON
ejpam-4721	23	4	present	present	VERB
ejpam-4721	23	5	a	a	DET
ejpam-4721	23	6	solution	solution	NOUN
ejpam-4721	23	7	algorithm	algorithm	NOUN
ejpam-4721	23	8	for	for	ADP
ejpam-4721	23	9	geometry	geometry	NOUN
ejpam-4721	23	10	problems	problem	NOUN
ejpam-4721	23	11	which	which	PRON
ejpam-4721	23	12	are	be	AUX
ejpam-4721	23	13	hard	hard	ADJ
ejpam-4721	23	14	to	to	PART
ejpam-4721	23	15	solve	solve	VERB
ejpam-4721	23	16	by	by	ADP
ejpam-4721	23	17	the	the	DET
ejpam-4721	23	18	method	method	NOUN
ejpam-4721	23	19	of	of	ADP
ejpam-4721	23	20	additional	additional	ADJ
ejpam-4721	23	21	constructions	construction	NOUN
ejpam-4721	23	22	.	.	PUNCT
ejpam-4721	24	1	in	in	ADP
ejpam-4721	24	2	conclusion	conclusion	NOUN
ejpam-4721	24	3	,	,	PUNCT
ejpam-4721	24	4	let	let	VERB
ejpam-4721	24	5	’s	’s	NOUN
ejpam-4721	24	6	mention	mention	VERB
ejpam-4721	24	7	the	the	DET
ejpam-4721	24	8	works	work	NOUN
ejpam-4721	24	9	[	[	X
ejpam-4721	24	10	1–3	1–3	NOUN
ejpam-4721	24	11	,	,	PUNCT
ejpam-4721	24	12	5	5	NUM
ejpam-4721	24	13	,	,	PUNCT
ejpam-4721	24	14	7	7	NUM
ejpam-4721	24	15	]	]	PUNCT
ejpam-4721	24	16	and	and	CCONJ
ejpam-4721	25	1	[	[	X
ejpam-4721	25	2	6	6	NUM
ejpam-4721	25	3	]	]	PUNCT
ejpam-4721	25	4	,	,	PUNCT
ejpam-4721	25	5	which	which	PRON
ejpam-4721	25	6	deal	deal	VERB
ejpam-4721	25	7	with	with	ADP
ejpam-4721	25	8	the	the	DET
ejpam-4721	25	9	method	method	NOUN
ejpam-4721	25	10	of	of	ADP
ejpam-4721	25	11	additional	additional	ADJ
ejpam-4721	25	12	constructions	construction	NOUN
ejpam-4721	25	13	.	.	PUNCT
ejpam-4721	26	1	we	we	PRON
ejpam-4721	26	2	solve	solve	VERB
ejpam-4721	26	3	some	some	PRON
ejpam-4721	26	4	of	of	ADP
ejpam-4721	26	5	problems	problem	NOUN
ejpam-4721	26	6	considered	consider	VERB
ejpam-4721	26	7	in	in	ADP
ejpam-4721	26	8	these	these	DET
ejpam-4721	26	9	works	work	NOUN
ejpam-4721	26	10	by	by	ADP
ejpam-4721	26	11	using	use	VERB
ejpam-4721	26	12	our	our	PRON
ejpam-4721	26	13	new	new	ADJ
ejpam-4721	26	14	method	method	NOUN
ejpam-4721	26	15	.	.	PUNCT
ejpam-4721	27	1	2	2	X
ejpam-4721	27	2	.	.	X
ejpam-4721	27	3	the	the	DET
ejpam-4721	27	4	method	method	NOUN
ejpam-4721	27	5	let	let	VERB
ejpam-4721	27	6	’s	’s	NOUN
ejpam-4721	27	7	illustrate	illustrate	VERB
ejpam-4721	27	8	our	our	PRON
ejpam-4721	27	9	new	new	ADJ
ejpam-4721	27	10	method	method	NOUN
ejpam-4721	27	11	on	on	ADP
ejpam-4721	27	12	the	the	DET
ejpam-4721	27	13	problem	problem	NOUN
ejpam-4721	27	14	solved	solve	VERB
ejpam-4721	27	15	by	by	ADP
ejpam-4721	27	16	using	use	VERB
ejpam-4721	27	17	the	the	DET
ejpam-4721	27	18	method	method	NOUN
ejpam-4721	27	19	of	of	ADP
ejpam-4721	27	20	additional	additional	ADJ
ejpam-4721	27	21	constructions	construction	NOUN
ejpam-4721	27	22	in	in	ADP
ejpam-4721	27	23	[	[	X
ejpam-4721	27	24	4	4	NUM
ejpam-4721	27	25	]	]	PUNCT
ejpam-4721	27	26	.	.	PUNCT
ejpam-4721	28	1	problem	problem	NOUN
ejpam-4721	28	2	1	1	NUM
ejpam-4721	28	3	.	.	PUNCT
ejpam-4721	29	1	the	the	DET
ejpam-4721	29	2	point	point	NOUN
ejpam-4721	29	3	m	m	AUX
ejpam-4721	29	4	is	be	AUX
ejpam-4721	29	5	given	give	VERB
ejpam-4721	29	6	inside	inside	ADP
ejpam-4721	29	7	the	the	DET
ejpam-4721	29	8	triangle	triangle	NOUN
ejpam-4721	29	9	abc	abc	PROPN
ejpam-4721	29	10	so	so	SCONJ
ejpam-4721	29	11	that	that	SCONJ
ejpam-4721	29	12	∠abm	∠abm	PROPN
ejpam-4721	29	13	=	=	SYM
ejpam-4721	29	14	40	40	NUM
ejpam-4721	29	15	◦	◦	NOUN
ejpam-4721	29	16	,	,	PUNCT
ejpam-4721	29	17	∠cbm	∠cbm	PROPN
ejpam-4721	29	18	=	=	SYM
ejpam-4721	29	19	10	10	NUM
ejpam-4721	29	20	◦	◦	NOUN
ejpam-4721	29	21	,	,	PUNCT
ejpam-4721	29	22	∠acm	∠acm	PROPN
ejpam-4721	29	23	=	=	SYM
ejpam-4721	29	24	20	20	NUM
ejpam-4721	29	25	◦	◦	NOUN
ejpam-4721	29	26	,	,	PUNCT
ejpam-4721	29	27	∠bcm	∠bcm	PROPN
ejpam-4721	29	28	=	=	SYM
ejpam-4721	29	29	10	10	NUM
ejpam-4721	29	30	◦	◦	NOUN
ejpam-4721	29	31	(	(	PUNCT
ejpam-4721	29	32	fig.1	fig.1	PROPN
ejpam-4721	29	33	)	)	PUNCT
ejpam-4721	29	34	.	.	PUNCT
ejpam-4721	30	1	prove	prove	VERB
ejpam-4721	30	2	that	that	SCONJ
ejpam-4721	30	3	∠cam	∠cam	PRON
ejpam-4721	30	4	=	=	SYM
ejpam-4721	30	5	30	30	NUM
ejpam-4721	30	6	◦	◦	NOUN
ejpam-4721	30	7	.	.	PUNCT
ejpam-4721	31	1	before	before	ADP
ejpam-4721	31	2	proceeding	proceed	VERB
ejpam-4721	31	3	to	to	PART
ejpam-4721	31	4	solve	solve	VERB
ejpam-4721	31	5	this	this	DET
ejpam-4721	31	6	problem	problem	NOUN
ejpam-4721	31	7	by	by	ADP
ejpam-4721	31	8	our	our	PRON
ejpam-4721	31	9	method	method	NOUN
ejpam-4721	31	10	,	,	PUNCT
ejpam-4721	31	11	let	let	VERB
ejpam-4721	31	12	’s	’s	PRON
ejpam-4721	31	13	recall	recall	VERB
ejpam-4721	31	14	how	how	SCONJ
ejpam-4721	31	15	it	it	PRON
ejpam-4721	31	16	was	be	AUX
ejpam-4721	31	17	solved	solve	VERB
ejpam-4721	31	18	by	by	ADP
ejpam-4721	31	19	the	the	DET
ejpam-4721	31	20	method	method	NOUN
ejpam-4721	31	21	of	of	ADP
ejpam-4721	31	22	additional	additional	ADJ
ejpam-4721	31	23	constructions	construction	NOUN
ejpam-4721	31	24	in	in	ADP
ejpam-4721	31	25	[	[	X
ejpam-4721	31	26	4	4	NUM
ejpam-4721	31	27	]	]	PUNCT
ejpam-4721	31	28	.	.	PUNCT
ejpam-4721	32	1	let	let	VERB
ejpam-4721	32	2	the	the	DET
ejpam-4721	32	3	circle	circle	NOUN
ejpam-4721	32	4	centered	center	VERB
ejpam-4721	32	5	at	at	ADP
ejpam-4721	32	6	m	m	PROPN
ejpam-4721	32	7	with	with	ADP
ejpam-4721	32	8	a	a	DET
ejpam-4721	32	9	radius	radius	NOUN
ejpam-4721	32	10	bm	bm	NOUN
ejpam-4721	32	11	=	=	PROPN
ejpam-4721	32	12	cm	cm	PROPN
ejpam-4721	32	13	intersect	intersect	VERB
ejpam-4721	32	14	the	the	DET
ejpam-4721	32	15	continuation	continuation	NOUN
ejpam-4721	32	16	of	of	ADP
ejpam-4721	32	17	ac	ac	PROPN
ejpam-4721	32	18	at	at	ADP
ejpam-4721	32	19	the	the	DET
ejpam-4721	32	20	point	point	NOUN
ejpam-4721	33	1	d	d	X
ejpam-4721	33	2	.	.	PUNCT
ejpam-4721	34	1	then	then	ADV
ejpam-4721	34	2	,	,	PUNCT
ejpam-4721	34	3	as	as	ADP
ejpam-4721	34	4	dm	dm	PROPN
ejpam-4721	34	5	=	=	PUNCT
ejpam-4721	34	6	cm	cm	NOUN
ejpam-4721	34	7	,	,	PUNCT
ejpam-4721	34	8	the	the	DET
ejpam-4721	34	9	triangle	triangle	NOUN
ejpam-4721	34	10	cmd	cmd	NOUN
ejpam-4721	34	11	is	be	AUX
ejpam-4721	34	12	equilateral	equilateral	ADJ
ejpam-4721	34	13	and	and	CCONJ
ejpam-4721	34	14	∠mdc	∠mdc	PROPN
ejpam-4721	34	15	=	=	PUNCT
ejpam-4721	34	16	∠mca	∠mca	PROPN
ejpam-4721	34	17	=	=	SYM
ejpam-4721	34	18	20	20	NUM
ejpam-4721	34	19	◦	◦	NOUN
ejpam-4721	34	20	(	(	PUNCT
ejpam-4721	34	21	fig.2	fig.2	PROPN
ejpam-4721	34	22	)	)	PUNCT
ejpam-4721	34	23	.	.	PUNCT
ejpam-4721	35	1	if	if	SCONJ
ejpam-4721	35	2	we	we	PRON
ejpam-4721	35	3	join	join	VERB
ejpam-4721	35	4	the	the	DET
ejpam-4721	35	5	points	point	NOUN
ejpam-4721	35	6	d	d	NOUN
ejpam-4721	35	7	and	and	CCONJ
ejpam-4721	35	8	b	b	NOUN
ejpam-4721	35	9	,	,	PUNCT
ejpam-4721	35	10	then	then	ADV
ejpam-4721	35	11	the	the	DET
ejpam-4721	35	12	triangle	triangle	NOUN
ejpam-4721	35	13	bdm	bdm	NOUN
ejpam-4721	35	14	becomes	become	VERB
ejpam-4721	35	15	equilateral	equilateral	ADJ
ejpam-4721	35	16	,	,	PUNCT
ejpam-4721	35	17	because	because	SCONJ
ejpam-4721	35	18	∠bmc	∠bmc	PROPN
ejpam-4721	35	19	=	=	SYM
ejpam-4721	35	20	160	160	NUM
ejpam-4721	35	21	◦	◦	NOUN
ejpam-4721	35	22	and	and	CCONJ
ejpam-4721	35	23	∠cmd	∠cmd	NOUN
ejpam-4721	35	24	=	=	SYM
ejpam-4721	35	25	140	140	NUM
ejpam-4721	35	26	◦	◦	NOUN
ejpam-4721	35	27	.	.	PUNCT
ejpam-4721	36	1	in	in	ADP
ejpam-4721	36	2	the	the	DET
ejpam-4721	36	3	triangle	triangle	NOUN
ejpam-4721	36	4	abd	abd	PROPN
ejpam-4721	36	5	,	,	PUNCT
ejpam-4721	36	6	we	we	PRON
ejpam-4721	36	7	find	find	VERB
ejpam-4721	36	8	∠bad	∠bad	PROPN
ejpam-4721	36	9	=	=	NOUN
ejpam-4721	36	10	180	180	NUM
ejpam-4721	36	11	◦	◦	NOUN
ejpam-4721	36	12	−(20	−(20	NOUN
ejpam-4721	36	13	◦	◦	NOUN
ejpam-4721	36	14	+	+	NOUN
ejpam-4721	36	15	80	80	NUM
ejpam-4721	36	16	◦	◦	NOUN
ejpam-4721	36	17	)	)	PUNCT
ejpam-4721	36	18	=	=	SYM
ejpam-4721	36	19	80	80	NUM
ejpam-4721	36	20	◦	◦	NOUN
ejpam-4721	36	21	.	.	PUNCT
ejpam-4721	37	1	hence	hence	ADV
ejpam-4721	37	2	,	,	PUNCT
ejpam-4721	37	3	bd	bd	PROPN
ejpam-4721	37	4	=	=	NOUN
ejpam-4721	37	5	ad	ad	NOUN
ejpam-4721	37	6	.	.	PUNCT
ejpam-4721	38	1	on	on	ADP
ejpam-4721	38	2	the	the	DET
ejpam-4721	38	3	other	other	ADJ
ejpam-4721	38	4	hand	hand	NOUN
ejpam-4721	38	5	,	,	PUNCT
ejpam-4721	38	6	as	as	ADP
ejpam-4721	38	7	bd	bd	PROPN
ejpam-4721	38	8	=	=	PROPN
ejpam-4721	38	9	bm	bm	PROPN
ejpam-4721	38	10	,	,	PUNCT
ejpam-4721	38	11	we	we	PRON
ejpam-4721	38	12	have	have	VERB
ejpam-4721	38	13	ab	ab	PROPN
ejpam-4721	38	14	=	=	SYM
ejpam-4721	38	15	bm	bm	PROPN
ejpam-4721	38	16	,	,	PUNCT
ejpam-4721	38	17	i.e.	i.e.	X
ejpam-4721	38	18	the	the	DET
ejpam-4721	38	19	triangle	triangle	NOUN
ejpam-4721	38	20	abm	abm	PROPN
ejpam-4721	38	21	is	be	AUX
ejpam-4721	38	22	isosceles	isoscele	NOUN
ejpam-4721	38	23	.	.	PUNCT
ejpam-4721	39	1	since	since	SCONJ
ejpam-4721	39	2	the	the	DET
ejpam-4721	39	3	angle	angle	NOUN
ejpam-4721	39	4	at	at	ADP
ejpam-4721	39	5	the	the	DET
ejpam-4721	39	6	vertex	vertex	NOUN
ejpam-4721	39	7	of	of	ADP
ejpam-4721	39	8	this	this	DET
ejpam-4721	39	9	triangle	triangle	NOUN
ejpam-4721	39	10	is	be	AUX
ejpam-4721	39	11	equal	equal	ADJ
ejpam-4721	39	12	to	to	ADP
ejpam-4721	39	13	40	40	NUM
ejpam-4721	39	14	◦	◦	NOUN
ejpam-4721	39	15	,	,	PUNCT
ejpam-4721	39	16	the	the	DET
ejpam-4721	39	17	adjacent	adjacent	ADJ
ejpam-4721	39	18	angles	angle	NOUN
ejpam-4721	39	19	at	at	ADP
ejpam-4721	39	20	the	the	DET
ejpam-4721	39	21	base	base	NOUN
ejpam-4721	39	22	are	be	AUX
ejpam-4721	39	23	equal	equal	ADJ
ejpam-4721	39	24	to	to	ADP
ejpam-4721	39	25	70	70	NUM
ejpam-4721	39	26	◦	◦	NOUN
ejpam-4721	39	27	.	.	PUNCT
ejpam-4721	40	1	consequently	consequently	ADV
ejpam-4721	40	2	,	,	PUNCT
ejpam-4721	40	3	∠bam	∠bam	PROPN
ejpam-4721	40	4	=	=	SYM
ejpam-4721	40	5	70	70	NUM
ejpam-4721	40	6	◦	◦	NOUN
ejpam-4721	40	7	,	,	PUNCT
ejpam-4721	40	8	and	and	CCONJ
ejpam-4721	40	9	therefore	therefore	ADV
ejpam-4721	40	10	,	,	PUNCT
ejpam-4721	40	11	∠cam	∠cam	PROPN
ejpam-4721	40	12	=	=	SYM
ejpam-4721	40	13	30	30	NUM
ejpam-4721	40	14	◦	◦	NOUN
ejpam-4721	40	15	.	.	PUNCT
ejpam-4721	41	1	now	now	ADV
ejpam-4721	41	2	let	let	VERB
ejpam-4721	41	3	’s	’s	NOUN
ejpam-4721	41	4	solve	solve	VERB
ejpam-4721	41	5	this	this	DET
ejpam-4721	41	6	problem	problem	NOUN
ejpam-4721	41	7	by	by	ADP
ejpam-4721	41	8	our	our	PRON
ejpam-4721	41	9	method	method	NOUN
ejpam-4721	41	10	.	.	PUNCT
ejpam-4721	42	1	s.	s.	PROPN
ejpam-4721	42	2	j.aliyev	j.aliyev	PROPN
ejpam-4721	42	3	,	,	PUNCT
ejpam-4721	42	4	m.	m.	PROPN
ejpam-4721	42	5	n.heydarova	n.heydarova	PROPN
ejpam-4721	42	6	,	,	PUNCT
ejpam-4721	42	7	s.	s.	PROPN
ejpam-4721	42	8	m.aghazade	m.aghazade	PROPN
ejpam-4721	42	9	/	/	SYM
ejpam-4721	42	10	eur	eur	PROPN
ejpam-4721	42	11	.	.	PUNCT
ejpam-4721	43	1	j.	j.	PROPN
ejpam-4721	43	2	pure	pure	PROPN
ejpam-4721	43	3	appl	appl	PROPN
ejpam-4721	43	4	.	.	PROPN
ejpam-4721	43	5	math	math	PROPN
ejpam-4721	43	6	,	,	PUNCT
ejpam-4721	43	7	16	16	NUM
ejpam-4721	43	8	(	(	PUNCT
ejpam-4721	43	9	2	2	NUM
ejpam-4721	43	10	)	)	PUNCT
ejpam-4721	43	11	(	(	PUNCT
ejpam-4721	43	12	2023	2023	NUM
ejpam-4721	43	13	)	)	PUNCT
ejpam-4721	43	14	,	,	PUNCT
ejpam-4721	43	15	1110	1110	NUM
ejpam-4721	43	16	-	-	SYM
ejpam-4721	43	17	1117	1117	NUM
ejpam-4721	43	18	1112	1112	NUM
ejpam-4721	43	19	figure	figure	NOUN
ejpam-4721	43	20	2	2	NUM
ejpam-4721	43	21	:	:	PUNCT
ejpam-4721	43	22	(	(	PUNCT
ejpam-4721	43	23	triangle	triangle	NOUN
ejpam-4721	43	24	bdm	bdm	NOUN
ejpam-4721	43	25	is	be	AUX
ejpam-4721	43	26	equilateral	equilateral	ADJ
ejpam-4721	43	27	,	,	PUNCT
ejpam-4721	43	28	while	while	SCONJ
ejpam-4721	43	29	triangles	triangle	NOUN
ejpam-4721	43	30	abd	abd	PROPN
ejpam-4721	43	31	and	and	CCONJ
ejpam-4721	43	32	abm	abm	PROPN
ejpam-4721	43	33	are	be	AUX
ejpam-4721	43	34	isosceles	isoscele	NOUN
ejpam-4721	43	35	)	)	PUNCT
ejpam-4721	43	36	divide	divide	VERB
ejpam-4721	43	37	the	the	DET
ejpam-4721	43	38	circle	circle	NOUN
ejpam-4721	43	39	into	into	ADP
ejpam-4721	43	40	18	18	NUM
ejpam-4721	43	41	equal	equal	ADJ
ejpam-4721	43	42	parts	part	NOUN
ejpam-4721	43	43	and	and	CCONJ
ejpam-4721	43	44	name	name	VERB
ejpam-4721	43	45	the	the	DET
ejpam-4721	43	46	division	division	NOUN
ejpam-4721	43	47	points	point	NOUN
ejpam-4721	43	48	.	.	PUNCT
ejpam-4721	44	1	degree	degree	NOUN
ejpam-4721	44	2	measure	measure	NOUN
ejpam-4721	44	3	of	of	ADP
ejpam-4721	44	4	the	the	DET
ejpam-4721	44	5	arc	arc	NOUN
ejpam-4721	44	6	between	between	ADP
ejpam-4721	44	7	two	two	NUM
ejpam-4721	44	8	consecutive	consecutive	ADJ
ejpam-4721	44	9	points	point	NOUN
ejpam-4721	44	10	is	be	AUX
ejpam-4721	44	11	equal	equal	ADJ
ejpam-4721	44	12	to	to	ADP
ejpam-4721	44	13	360	360	NUM
ejpam-4721	44	14	◦	◦	NOUN
ejpam-4721	44	15	18	18	NUM
ejpam-4721	44	16	=	=	SYM
ejpam-4721	44	17	20	20	NUM
ejpam-4721	44	18	◦	◦	NOUN
ejpam-4721	44	19	.	.	PUNCT
ejpam-4721	45	1	if	if	SCONJ
ejpam-4721	45	2	we	we	PRON
ejpam-4721	45	3	place	place	VERB
ejpam-4721	45	4	the	the	DET
ejpam-4721	45	5	triangle	triangle	NOUN
ejpam-4721	45	6	abc	abc	PROPN
ejpam-4721	45	7	inside	inside	ADP
ejpam-4721	45	8	the	the	DET
ejpam-4721	45	9	circle	circle	NOUN
ejpam-4721	45	10	as	as	SCONJ
ejpam-4721	45	11	shown	show	VERB
ejpam-4721	45	12	on	on	ADP
ejpam-4721	45	13	fig.3	fig.3	PROPN
ejpam-4721	45	14	(	(	PUNCT
ejpam-4721	45	15	a	a	DET
ejpam-4721	45	16	≡	≡	PROPN
ejpam-4721	45	17	c18	c18	NOUN
ejpam-4721	45	18	,	,	PUNCT
ejpam-4721	45	19	b	b	PROPN
ejpam-4721	45	20	≡	≡	PROPN
ejpam-4721	45	21	c15	c15	NOUN
ejpam-4721	45	22	,	,	PUNCT
ejpam-4721	45	23	c	c	PROPN
ejpam-4721	45	24	≡	≡	PROPN
ejpam-4721	45	25	c5	c5	PROPN
ejpam-4721	45	26	)	)	PUNCT
ejpam-4721	45	27	,	,	PUNCT
ejpam-4721	45	28	then	then	ADV
ejpam-4721	45	29	the	the	DET
ejpam-4721	45	30	conditions	condition	NOUN
ejpam-4721	45	31	of	of	ADP
ejpam-4721	45	32	the	the	DET
ejpam-4721	45	33	problem	problem	NOUN
ejpam-4721	45	34	are	be	AUX
ejpam-4721	45	35	satisfied	satisfied	ADJ
ejpam-4721	45	36	:	:	PUNCT
ejpam-4721	45	37	∠c18c14c4	∠c18c14c4	SYM
ejpam-4721	45	38	=	=	SYM
ejpam-4721	45	39	40	40	NUM
ejpam-4721	45	40	◦	◦	NOUN
ejpam-4721	45	41	,	,	PUNCT
ejpam-4721	45	42	∠c5c15c4	∠c5c15c4	PROPN
ejpam-4721	45	43	=	=	SYM
ejpam-4721	45	44	10	10	NUM
ejpam-4721	45	45	◦	◦	NOUN
ejpam-4721	45	46	,	,	PUNCT
ejpam-4721	45	47	∠c18c5c16	∠c18c5c16	NOUN
ejpam-4721	45	48	=	=	SYM
ejpam-4721	45	49	20	20	NUM
ejpam-4721	45	50	◦	◦	NOUN
ejpam-4721	45	51	,	,	PUNCT
ejpam-4721	45	52	∠c15c5c16	∠c15c5c16	NOUN
ejpam-4721	45	53	=	=	PUNCT
ejpam-4721	45	54	10	10	NUM
ejpam-4721	45	55	◦	◦	NOUN
ejpam-4721	45	56	.	.	PUNCT
ejpam-4721	46	1	from	from	ADP
ejpam-4721	46	2	fig.3	fig.3	PROPN
ejpam-4721	46	3	we	we	PRON
ejpam-4721	46	4	can	can	AUX
ejpam-4721	46	5	see	see	VERB
ejpam-4721	46	6	that	that	SCONJ
ejpam-4721	46	7	the	the	DET
ejpam-4721	46	8	sought	seek	VERB
ejpam-4721	46	9	angle	angle	NOUN
ejpam-4721	46	10	c5c18c8	c5c18c8	NOUN
ejpam-4721	46	11	is	be	AUX
ejpam-4721	46	12	equal	equal	ADJ
ejpam-4721	46	13	to	to	ADP
ejpam-4721	46	14	30	30	NUM
ejpam-4721	46	15	◦	◦	NOUN
ejpam-4721	46	16	.	.	PUNCT
ejpam-4721	47	1	consequently	consequently	ADV
ejpam-4721	47	2	,	,	PUNCT
ejpam-4721	47	3	the	the	DET
ejpam-4721	47	4	considered	consider	VERB
ejpam-4721	47	5	problem	problem	NOUN
ejpam-4721	47	6	is	be	AUX
ejpam-4721	47	7	equivalent	equivalent	ADJ
ejpam-4721	47	8	to	to	ADP
ejpam-4721	47	9	the	the	DET
ejpam-4721	47	10	following	follow	VERB
ejpam-4721	47	11	statement	statement	NOUN
ejpam-4721	47	12	:	:	PUNCT
ejpam-4721	47	13	in	in	ADP
ejpam-4721	47	14	the	the	DET
ejpam-4721	47	15	regular	regular	ADJ
ejpam-4721	47	16	octadecagon	octadecagon	NOUN
ejpam-4721	47	17	,	,	PUNCT
ejpam-4721	47	18	the	the	DET
ejpam-4721	47	19	diagonals	diagonal	NOUN
ejpam-4721	47	20	c4c15	c4c15	VERB
ejpam-4721	47	21	,	,	PUNCT
ejpam-4721	47	22	c5c16	c5c16	NOUN
ejpam-4721	47	23	and	and	CCONJ
ejpam-4721	47	24	c8c18	c8c18	NOUN
ejpam-4721	47	25	intersect	intersect	ADJ
ejpam-4721	47	26	each	each	DET
ejpam-4721	47	27	other	other	ADJ
ejpam-4721	47	28	at	at	ADP
ejpam-4721	47	29	one	one	NUM
ejpam-4721	47	30	point	point	NOUN
ejpam-4721	47	31	.	.	PUNCT
ejpam-4721	48	1	to	to	PART
ejpam-4721	48	2	verify	verify	VERB
ejpam-4721	48	3	the	the	DET
ejpam-4721	48	4	intersection	intersection	NOUN
ejpam-4721	48	5	of	of	ADP
ejpam-4721	48	6	these	these	DET
ejpam-4721	48	7	three	three	NUM
ejpam-4721	48	8	diagonals	diagonal	NOUN
ejpam-4721	48	9	at	at	ADP
ejpam-4721	48	10	one	one	NUM
ejpam-4721	48	11	point	point	NOUN
ejpam-4721	48	12	,	,	PUNCT
ejpam-4721	48	13	it	it	PRON
ejpam-4721	48	14	is	be	AUX
ejpam-4721	48	15	convenient	convenient	ADJ
ejpam-4721	48	16	to	to	PART
ejpam-4721	48	17	use	use	VERB
ejpam-4721	48	18	the	the	DET
ejpam-4721	48	19	following	follow	VERB
ejpam-4721	48	20	trigonometric	trigonometric	ADJ
ejpam-4721	48	21	(	(	PUNCT
ejpam-4721	48	22	angular	angular	ADJ
ejpam-4721	48	23	)	)	PUNCT
ejpam-4721	48	24	theorem	theorem	NOUN
ejpam-4721	48	25	of	of	ADP
ejpam-4721	48	26	giovanni	giovanni	PROPN
ejpam-4721	48	27	ceva	ceva	PROPN
ejpam-4721	49	1	[	[	X
ejpam-4721	49	2	6	6	NUM
ejpam-4721	49	3	]	]	PUNCT
ejpam-4721	49	4	.	.	PUNCT
ejpam-4721	50	1	theorem	theorem	VERB
ejpam-4721	50	2	.	.	PUNCT
ejpam-4721	51	1	let	let	VERB
ejpam-4721	51	2	the	the	DET
ejpam-4721	51	3	points	point	NOUN
ejpam-4721	51	4	a1	a1	NOUN
ejpam-4721	51	5	,	,	PUNCT
ejpam-4721	51	6	b1	b1	NOUN
ejpam-4721	51	7	,	,	PUNCT
ejpam-4721	51	8	c1	c1	PROPN
ejpam-4721	51	9	be	be	AUX
ejpam-4721	51	10	given	give	VERB
ejpam-4721	51	11	on	on	ADP
ejpam-4721	51	12	the	the	DET
ejpam-4721	51	13	sides	side	NOUN
ejpam-4721	51	14	bc	bc	PROPN
ejpam-4721	51	15	,	,	PUNCT
ejpam-4721	51	16	ac	ac	PROPN
ejpam-4721	51	17	,	,	PUNCT
ejpam-4721	51	18	ab	ab	PROPN
ejpam-4721	51	19	of	of	ADP
ejpam-4721	51	20	the	the	DET
ejpam-4721	51	21	triangle	triangle	NOUN
ejpam-4721	51	22	abc	abc	PROPN
ejpam-4721	51	23	,	,	PUNCT
ejpam-4721	51	24	respectively	respectively	ADV
ejpam-4721	51	25	.	.	PUNCT
ejpam-4721	52	1	then	then	ADV
ejpam-4721	52	2	the	the	DET
ejpam-4721	52	3	segments	segments	PROPN
ejpam-4721	52	4	aa1	aa1	PROPN
ejpam-4721	52	5	,	,	PUNCT
ejpam-4721	52	6	bb1	bb1	PROPN
ejpam-4721	52	7	and	and	CCONJ
ejpam-4721	52	8	cc1	cc1	PROPN
ejpam-4721	52	9	intersect	intersect	ADJ
ejpam-4721	52	10	each	each	DET
ejpam-4721	52	11	other	other	ADJ
ejpam-4721	52	12	at	at	ADP
ejpam-4721	52	13	one	one	NUM
ejpam-4721	52	14	point	point	NOUN
ejpam-4721	52	15	if	if	SCONJ
ejpam-4721	52	16	and	and	CCONJ
ejpam-4721	52	17	only	only	ADV
ejpam-4721	52	18	if	if	SCONJ
ejpam-4721	52	19	(	(	PUNCT
ejpam-4721	52	20	fig.4	fig.4	PROPN
ejpam-4721	52	21	)	)	PUNCT
ejpam-4721	52	22	sin∠baa1	sin∠baa1	NOUN
ejpam-4721	52	23	sin∠caa1	sin∠caa1	PROPN
ejpam-4721	52	24	·	·	PUNCT
ejpam-4721	52	25	sin∠cbb1	sin∠cbb1	VERB
ejpam-4721	52	26	sin∠abb1	sin∠abb1	NOUN
ejpam-4721	52	27	·	·	PUNCT
ejpam-4721	52	28	sin∠acc1	sin∠acc1	NUM
ejpam-4721	52	29	sin∠bcc1	sin∠bcc1	NOUN
ejpam-4721	52	30	=	=	SYM
ejpam-4721	52	31	1	1	X
ejpam-4721	52	32	.	.	PUNCT
ejpam-4721	53	1	so	so	ADV
ejpam-4721	53	2	,	,	PUNCT
ejpam-4721	53	3	the	the	DET
ejpam-4721	53	4	verification	verification	NOUN
ejpam-4721	53	5	of	of	ADP
ejpam-4721	53	6	whether	whether	SCONJ
ejpam-4721	53	7	three	three	NUM
ejpam-4721	53	8	diagonals	diagonal	NOUN
ejpam-4721	53	9	c4c15	c4c15	VERB
ejpam-4721	53	10	,	,	PUNCT
ejpam-4721	53	11	c5c16	c5c16	NOUN
ejpam-4721	53	12	and	and	CCONJ
ejpam-4721	53	13	c8c18	c8c18	NOUN
ejpam-4721	53	14	on	on	ADP
ejpam-4721	53	15	fig.3	fig.3	PROPN
ejpam-4721	53	16	intersect	intersect	NOUN
ejpam-4721	53	17	each	each	DET
ejpam-4721	53	18	other	other	ADJ
ejpam-4721	53	19	at	at	ADP
ejpam-4721	53	20	one	one	NUM
ejpam-4721	53	21	point	point	NOUN
ejpam-4721	53	22	is	be	AUX
ejpam-4721	53	23	reduced	reduce	VERB
ejpam-4721	53	24	to	to	ADP
ejpam-4721	53	25	the	the	DET
ejpam-4721	53	26	verification	verification	NOUN
ejpam-4721	53	27	of	of	ADP
ejpam-4721	53	28	the	the	DET
ejpam-4721	53	29	following	follow	VERB
ejpam-4721	53	30	identity	identity	NOUN
ejpam-4721	53	31	:	:	PUNCT
ejpam-4721	53	32	sin10	sin10	PROPN
ejpam-4721	53	33	◦	◦	PROPN
ejpam-4721	53	34	sin40	sin40	PROPN
ejpam-4721	53	35	◦	◦	NOUN
ejpam-4721	53	36	·	·	PUNCT
ejpam-4721	53	37	sin20	sin20	PROPN
ejpam-4721	53	38	◦	◦	PROPN
ejpam-4721	53	39	sin10	sin10	PROPN
ejpam-4721	53	40	◦	◦	NOUN
ejpam-4721	53	41	·	·	PUNCT
ejpam-4721	53	42	sin70	sin70	PROPN
ejpam-4721	53	43	◦	◦	NOUN
ejpam-4721	53	44	sin30	sin30	VERB
ejpam-4721	53	45	◦	◦	NOUN
ejpam-4721	53	46	=	=	SYM
ejpam-4721	53	47	1	1	NUM
ejpam-4721	53	48	and	and	CCONJ
ejpam-4721	53	49	the	the	DET
ejpam-4721	53	50	validity	validity	NOUN
ejpam-4721	53	51	of	of	ADP
ejpam-4721	53	52	this	this	DET
ejpam-4721	53	53	identity	identity	NOUN
ejpam-4721	53	54	follows	follow	VERB
ejpam-4721	53	55	from	from	ADP
ejpam-4721	53	56	the	the	DET
ejpam-4721	53	57	equalities	equality	NOUN
ejpam-4721	53	58	sin70	sin70	VERB
ejpam-4721	53	59	◦	◦	NOUN
ejpam-4721	53	60	=	=	SYM
ejpam-4721	53	61	cos20	cos20	NOUN
ejpam-4721	53	62	◦	◦	NOUN
ejpam-4721	53	63	,	,	PUNCT
ejpam-4721	53	64	sin40	sin40	NOUN
ejpam-4721	53	65	◦	◦	NOUN
ejpam-4721	53	66	=	=	SYM
ejpam-4721	53	67	2sin20	2sin20	NOUN
ejpam-4721	53	68	◦	◦	NOUN
ejpam-4721	53	69	cos20	cos20	NOUN
ejpam-4721	53	70	◦	◦	NOUN
ejpam-4721	53	71	.	.	PUNCT
ejpam-4721	53	72	.	.	PUNCT
ejpam-4721	54	1	if	if	SCONJ
ejpam-4721	54	2	we	we	PRON
ejpam-4721	54	3	compare	compare	VERB
ejpam-4721	54	4	the	the	DET
ejpam-4721	54	5	above	above	ADJ
ejpam-4721	54	6	two	two	NUM
ejpam-4721	54	7	methods	method	NOUN
ejpam-4721	54	8	used	use	VERB
ejpam-4721	54	9	to	to	PART
ejpam-4721	54	10	solve	solve	VERB
ejpam-4721	54	11	problem	problem	NOUN
ejpam-4721	54	12	1	1	NUM
ejpam-4721	54	13	,	,	PUNCT
ejpam-4721	54	14	then	then	ADV
ejpam-4721	54	15	we	we	PRON
ejpam-4721	54	16	can	can	AUX
ejpam-4721	54	17	easily	easily	ADV
ejpam-4721	54	18	see	see	VERB
ejpam-4721	54	19	that	that	SCONJ
ejpam-4721	54	20	the	the	DET
ejpam-4721	54	21	second	second	ADJ
ejpam-4721	54	22	one	one	NOUN
ejpam-4721	54	23	is	be	AUX
ejpam-4721	54	24	simpler	simple	ADJ
ejpam-4721	54	25	and	and	CCONJ
ejpam-4721	54	26	more	more	ADV
ejpam-4721	54	27	effective	effective	ADJ
ejpam-4721	54	28	.	.	PUNCT
ejpam-4721	55	1	besides	besides	SCONJ
ejpam-4721	55	2	,	,	PUNCT
ejpam-4721	55	3	the	the	DET
ejpam-4721	55	4	first	first	ADJ
ejpam-4721	55	5	method	method	NOUN
ejpam-4721	55	6	requires	require	VERB
ejpam-4721	55	7	additional	additional	ADJ
ejpam-4721	55	8	constructions	construction	NOUN
ejpam-4721	55	9	,	,	PUNCT
ejpam-4721	55	10	while	while	SCONJ
ejpam-4721	55	11	the	the	DET
ejpam-4721	55	12	second	second	ADJ
ejpam-4721	55	13	one	one	NOUN
ejpam-4721	55	14	only	only	ADV
ejpam-4721	55	15	needs	need	VERB
ejpam-4721	55	16	the	the	DET
ejpam-4721	55	17	accurate	accurate	ADJ
ejpam-4721	55	18	drawing	drawing	NOUN
ejpam-4721	55	19	.	.	PUNCT
ejpam-4721	56	1	s.	s.	PROPN
ejpam-4721	56	2	j.aliyev	j.aliyev	PROPN
ejpam-4721	56	3	,	,	PUNCT
ejpam-4721	56	4	m.	m.	PROPN
ejpam-4721	56	5	n.heydarova	n.heydarova	PROPN
ejpam-4721	56	6	,	,	PUNCT
ejpam-4721	56	7	s.	s.	PROPN
ejpam-4721	56	8	m.aghazade	m.aghazade	PROPN
ejpam-4721	56	9	/	/	SYM
ejpam-4721	56	10	eur	eur	PROPN
ejpam-4721	56	11	.	.	PUNCT
ejpam-4721	57	1	j.	j.	PROPN
ejpam-4721	57	2	pure	pure	PROPN
ejpam-4721	57	3	appl	appl	PROPN
ejpam-4721	57	4	.	.	PROPN
ejpam-4721	57	5	math	math	PROPN
ejpam-4721	57	6	,	,	PUNCT
ejpam-4721	57	7	16	16	NUM
ejpam-4721	57	8	(	(	PUNCT
ejpam-4721	57	9	2	2	NUM
ejpam-4721	57	10	)	)	PUNCT
ejpam-4721	57	11	(	(	PUNCT
ejpam-4721	57	12	2023	2023	NUM
ejpam-4721	57	13	)	)	PUNCT
ejpam-4721	57	14	,	,	PUNCT
ejpam-4721	57	15	1110	1110	NUM
ejpam-4721	57	16	-	-	SYM
ejpam-4721	57	17	1117	1117	NUM
ejpam-4721	57	18	1113	1113	NUM
ejpam-4721	57	19	figure	figure	NOUN
ejpam-4721	57	20	3	3	NUM
ejpam-4721	57	21	:	:	PUNCT
ejpam-4721	57	22	(	(	PUNCT
ejpam-4721	57	23	triangle	triangle	PROPN
ejpam-4721	57	24	c18c15c5	c18c15c5	NOUN
ejpam-4721	57	25	,	,	PUNCT
ejpam-4721	57	26	equal	equal	ADJ
ejpam-4721	57	27	to	to	PART
ejpam-4721	57	28	triangle	triangle	VERB
ejpam-4721	57	29	abc	abc	PROPN
ejpam-4721	57	30	,	,	PUNCT
ejpam-4721	57	31	placed	place	VERB
ejpam-4721	57	32	inside	inside	ADP
ejpam-4721	57	33	the	the	DET
ejpam-4721	57	34	circle	circle	NOUN
ejpam-4721	57	35	)	)	PUNCT
ejpam-4721	57	36	this	this	DET
ejpam-4721	57	37	example	example	NOUN
ejpam-4721	57	38	shows	show	VERB
ejpam-4721	57	39	that	that	SCONJ
ejpam-4721	57	40	many	many	ADJ
ejpam-4721	57	41	problems	problem	NOUN
ejpam-4721	57	42	,	,	PUNCT
ejpam-4721	57	43	even	even	ADV
ejpam-4721	57	44	very	very	ADV
ejpam-4721	57	45	difficult	difficult	ADJ
ejpam-4721	57	46	ones	one	NOUN
ejpam-4721	57	47	,	,	PUNCT
ejpam-4721	57	48	can	can	AUX
ejpam-4721	57	49	be	be	AUX
ejpam-4721	57	50	solved	solve	VERB
ejpam-4721	57	51	using	use	VERB
ejpam-4721	57	52	one	one	NUM
ejpam-4721	57	53	property	property	NOUN
ejpam-4721	57	54	of	of	ADP
ejpam-4721	57	55	regular	regular	ADJ
ejpam-4721	57	56	polygon	polygon	NOUN
ejpam-4721	57	57	diagonals	diagonal	NOUN
ejpam-4721	57	58	:	:	PUNCT
ejpam-4721	57	59	property	property	NOUN
ejpam-4721	57	60	of	of	ADP
ejpam-4721	57	61	intersection	intersection	NOUN
ejpam-4721	57	62	at	at	ADP
ejpam-4721	57	63	one	one	NUM
ejpam-4721	57	64	point	point	NOUN
ejpam-4721	57	65	.	.	PUNCT
ejpam-4721	58	1	when	when	SCONJ
ejpam-4721	58	2	solving	solve	VERB
ejpam-4721	58	3	problem	problem	NOUN
ejpam-4721	58	4	1	1	NUM
ejpam-4721	58	5	by	by	ADP
ejpam-4721	58	6	our	our	PRON
ejpam-4721	58	7	method	method	NOUN
ejpam-4721	58	8	,	,	PUNCT
ejpam-4721	58	9	we	we	PRON
ejpam-4721	58	10	divided	divide	VERB
ejpam-4721	58	11	the	the	DET
ejpam-4721	58	12	circle	circle	NOUN
ejpam-4721	58	13	into	into	ADP
ejpam-4721	58	14	18	18	NUM
ejpam-4721	58	15	equal	equal	ADJ
ejpam-4721	58	16	parts	part	NOUN
ejpam-4721	58	17	.	.	PUNCT
ejpam-4721	59	1	this	this	PRON
ejpam-4721	59	2	is	be	AUX
ejpam-4721	59	3	because	because	SCONJ
ejpam-4721	59	4	the	the	DET
ejpam-4721	59	5	triangle	triangle	NOUN
ejpam-4721	59	6	in	in	ADP
ejpam-4721	59	7	this	this	DET
ejpam-4721	59	8	problem	problem	NOUN
ejpam-4721	59	9	has	have	VERB
ejpam-4721	59	10	the	the	DET
ejpam-4721	59	11	angles	angle	NOUN
ejpam-4721	59	12	which	which	PRON
ejpam-4721	59	13	are	be	AUX
ejpam-4721	59	14	the	the	DET
ejpam-4721	59	15	multiples	multiple	NOUN
ejpam-4721	59	16	of	of	ADP
ejpam-4721	59	17	10	10	NUM
ejpam-4721	59	18	◦	◦	NOUN
ejpam-4721	59	19	.	.	PUNCT
ejpam-4721	60	1	depending	depend	VERB
ejpam-4721	60	2	on	on	ADP
ejpam-4721	60	3	the	the	DET
ejpam-4721	60	4	sizes	size	NOUN
ejpam-4721	60	5	of	of	ADP
ejpam-4721	60	6	the	the	DET
ejpam-4721	60	7	angles	angle	NOUN
ejpam-4721	60	8	,	,	PUNCT
ejpam-4721	60	9	the	the	DET
ejpam-4721	60	10	problem	problem	NOUN
ejpam-4721	60	11	can	can	AUX
ejpam-4721	60	12	be	be	AUX
ejpam-4721	60	13	solved	solve	VERB
ejpam-4721	60	14	by	by	ADP
ejpam-4721	60	15	dividing	divide	VERB
ejpam-4721	60	16	the	the	DET
ejpam-4721	60	17	circle	circle	NOUN
ejpam-4721	60	18	into	into	ADP
ejpam-4721	60	19	less	less	ADJ
ejpam-4721	60	20	than	than	ADP
ejpam-4721	60	21	18	18	NUM
ejpam-4721	60	22	equal	equal	ADJ
ejpam-4721	60	23	parts	part	NOUN
ejpam-4721	60	24	.	.	PUNCT
ejpam-4721	61	1	for	for	ADP
ejpam-4721	61	2	example	example	NOUN
ejpam-4721	61	3	,	,	PUNCT
ejpam-4721	61	4	to	to	PART
ejpam-4721	61	5	solve	solve	VERB
ejpam-4721	61	6	the	the	DET
ejpam-4721	61	7	problem	problem	NOUN
ejpam-4721	61	8	below	below	ADV
ejpam-4721	61	9	,	,	PUNCT
ejpam-4721	61	10	we	we	PRON
ejpam-4721	61	11	will	will	AUX
ejpam-4721	61	12	divide	divide	VERB
ejpam-4721	61	13	the	the	DET
ejpam-4721	61	14	circle	circle	NOUN
ejpam-4721	61	15	into	into	ADP
ejpam-4721	61	16	12	12	NUM
ejpam-4721	61	17	equal	equal	ADJ
ejpam-4721	61	18	parts	part	NOUN
ejpam-4721	61	19	.	.	PUNCT
ejpam-4721	62	1	problem	problem	NOUN
ejpam-4721	62	2	2	2	NUM
ejpam-4721	62	3	.	.	PUNCT
ejpam-4721	63	1	the	the	DET
ejpam-4721	63	2	point	point	NOUN
ejpam-4721	63	3	m	m	AUX
ejpam-4721	63	4	is	be	AUX
ejpam-4721	63	5	given	give	VERB
ejpam-4721	63	6	inside	inside	ADP
ejpam-4721	63	7	the	the	DET
ejpam-4721	63	8	triangle	triangle	NOUN
ejpam-4721	63	9	abc	abc	PROPN
ejpam-4721	63	10	so	so	SCONJ
ejpam-4721	63	11	that	that	SCONJ
ejpam-4721	63	12	∠abm	∠abm	PROPN
ejpam-4721	63	13	=	=	SYM
ejpam-4721	63	14	∠cbm	∠cbm	VERB
ejpam-4721	63	15	=	=	SYM
ejpam-4721	63	16	∠bcm	∠bcm	PROPN
ejpam-4721	63	17	=	=	SYM
ejpam-4721	63	18	15	15	NUM
ejpam-4721	63	19	◦	◦	NOUN
ejpam-4721	63	20	and	and	CCONJ
ejpam-4721	63	21	∠acm	∠acm	PROPN
ejpam-4721	63	22	=	=	SYM
ejpam-4721	63	23	30	30	NUM
ejpam-4721	63	24	◦	◦	NOUN
ejpam-4721	63	25	(	(	PUNCT
ejpam-4721	63	26	fig.5	fig.5	PROPN
ejpam-4721	63	27	)	)	PUNCT
ejpam-4721	63	28	.	.	PUNCT
ejpam-4721	64	1	prove	prove	VERB
ejpam-4721	64	2	that	that	SCONJ
ejpam-4721	64	3	∠cam	∠cam	PROPN
ejpam-4721	64	4	=	=	SYM
ejpam-4721	64	5	75	75	NUM
ejpam-4721	64	6	◦	◦	NOUN
ejpam-4721	64	7	.	.	PUNCT
ejpam-4721	65	1	as	as	SCONJ
ejpam-4721	65	2	the	the	DET
ejpam-4721	65	3	angles	angle	NOUN
ejpam-4721	65	4	given	give	VERB
ejpam-4721	65	5	in	in	ADP
ejpam-4721	65	6	this	this	DET
ejpam-4721	65	7	problem	problem	NOUN
ejpam-4721	65	8	are	be	AUX
ejpam-4721	65	9	the	the	DET
ejpam-4721	65	10	multiples	multiple	NOUN
ejpam-4721	65	11	of	of	ADP
ejpam-4721	65	12	15	15	NUM
ejpam-4721	65	13	◦	◦	NOUN
ejpam-4721	65	14	,	,	PUNCT
ejpam-4721	65	15	we	we	PRON
ejpam-4721	65	16	divide	divide	VERB
ejpam-4721	65	17	the	the	DET
ejpam-4721	65	18	circle	circle	NOUN
ejpam-4721	65	19	into	into	ADP
ejpam-4721	65	20	12	12	NUM
ejpam-4721	65	21	,	,	PUNCT
ejpam-4721	65	22	not	not	PART
ejpam-4721	65	23	18	18	NUM
ejpam-4721	65	24	equal	equal	ADJ
ejpam-4721	65	25	parts	part	NOUN
ejpam-4721	65	26	.	.	PUNCT
ejpam-4721	65	27	degree	degree	NOUN
ejpam-4721	65	28	measure	measure	NOUN
ejpam-4721	65	29	of	of	ADP
ejpam-4721	65	30	the	the	DET
ejpam-4721	65	31	arc	arc	NOUN
ejpam-4721	65	32	between	between	ADP
ejpam-4721	65	33	two	two	NUM
ejpam-4721	65	34	consecutive	consecutive	ADJ
ejpam-4721	65	35	points	point	NOUN
ejpam-4721	65	36	is	be	AUX
ejpam-4721	65	37	360	360	NUM
ejpam-4721	65	38	◦	◦	NOUN
ejpam-4721	65	39	12	12	NUM
ejpam-4721	65	40	=	=	SYM
ejpam-4721	65	41	30	30	NUM
ejpam-4721	65	42	◦	◦	NOUN
ejpam-4721	65	43	.	.	PUNCT
ejpam-4721	66	1	if	if	SCONJ
ejpam-4721	66	2	we	we	PRON
ejpam-4721	66	3	place	place	VERB
ejpam-4721	66	4	the	the	DET
ejpam-4721	66	5	triangle	triangle	NOUN
ejpam-4721	66	6	abc	abc	PROPN
ejpam-4721	66	7	inside	inside	ADP
ejpam-4721	66	8	the	the	DET
ejpam-4721	66	9	circle	circle	NOUN
ejpam-4721	66	10	as	as	SCONJ
ejpam-4721	66	11	shown	show	VERB
ejpam-4721	66	12	on	on	ADP
ejpam-4721	66	13	fig.6	fig.6	PROPN
ejpam-4721	66	14	(	(	PUNCT
ejpam-4721	66	15	a	a	DET
ejpam-4721	66	16	≡	≡	PROPN
ejpam-4721	66	17	p1	p1	PROPN
ejpam-4721	66	18	,	,	PUNCT
ejpam-4721	66	19	b	b	PROPN
ejpam-4721	66	20	≡	≡	PROPN
ejpam-4721	66	21	p10	p10	PROPN
ejpam-4721	66	22	,	,	PUNCT
ejpam-4721	66	23	c	c	PROPN
ejpam-4721	66	24	≡	≡	PROPN
ejpam-4721	66	25	p3	p3	PROPN
ejpam-4721	66	26	)	)	PUNCT
ejpam-4721	66	27	,	,	PUNCT
ejpam-4721	66	28	then	then	ADV
ejpam-4721	66	29	the	the	DET
ejpam-4721	66	30	conditions	condition	NOUN
ejpam-4721	66	31	of	of	ADP
ejpam-4721	66	32	the	the	DET
ejpam-4721	66	33	problem	problem	NOUN
ejpam-4721	66	34	are	be	AUX
ejpam-4721	66	35	satisfied	satisfied	ADJ
ejpam-4721	66	36	:	:	PUNCT
ejpam-4721	66	37	∠p1p10p2	∠p1p10p2	PROPN
ejpam-4721	66	38	=	=	SYM
ejpam-4721	66	39	∠p3p10p2	∠p3p10p2	NUM
ejpam-4721	66	40	=	=	SYM
ejpam-4721	66	41	∠p10p3p11	∠p10p3p11	NOUN
ejpam-4721	66	42	=	=	SYM
ejpam-4721	66	43	15	15	NUM
ejpam-4721	66	44	◦	◦	NOUN
ejpam-4721	66	45	,∠p1p3p11	,∠p1p3p11	PUNCT
ejpam-4721	66	46	=	=	SYM
ejpam-4721	66	47	30	30	NUM
ejpam-4721	66	48	◦	◦	NOUN
ejpam-4721	66	49	.	.	PUNCT
ejpam-4721	67	1	from	from	ADP
ejpam-4721	67	2	fig.6	fig.6	PROPN
ejpam-4721	67	3	we	we	PRON
ejpam-4721	67	4	can	can	AUX
ejpam-4721	67	5	see	see	VERB
ejpam-4721	67	6	that	that	SCONJ
ejpam-4721	67	7	the	the	DET
ejpam-4721	67	8	sought	seek	VERB
ejpam-4721	67	9	angle	angle	NOUN
ejpam-4721	67	10	p8p1p3	p8p1p3	PROPN
ejpam-4721	67	11	is	be	AUX
ejpam-4721	67	12	equal	equal	ADJ
ejpam-4721	67	13	to	to	ADP
ejpam-4721	67	14	75	75	NUM
ejpam-4721	67	15	◦	◦	NOUN
ejpam-4721	67	16	.	.	PUNCT
ejpam-4721	68	1	consequently	consequently	ADV
ejpam-4721	68	2	,	,	PUNCT
ejpam-4721	68	3	the	the	DET
ejpam-4721	68	4	considered	consider	VERB
ejpam-4721	68	5	problem	problem	NOUN
ejpam-4721	68	6	is	be	AUX
ejpam-4721	68	7	equivalent	equivalent	ADJ
ejpam-4721	68	8	to	to	ADP
ejpam-4721	68	9	the	the	DET
ejpam-4721	68	10	following	follow	VERB
ejpam-4721	68	11	statement	statement	NOUN
ejpam-4721	68	12	:	:	PUNCT
ejpam-4721	68	13	in	in	ADP
ejpam-4721	68	14	the	the	DET
ejpam-4721	68	15	regular	regular	ADJ
ejpam-4721	68	16	dodecagon	dodecagon	NOUN
ejpam-4721	68	17	,	,	PUNCT
ejpam-4721	68	18	the	the	DET
ejpam-4721	68	19	diagonals	diagonal	NOUN
ejpam-4721	68	20	p1p8	p1p8	NOUN
ejpam-4721	68	21	,	,	PUNCT
ejpam-4721	68	22	p2p10	p2p10	NOUN
ejpam-4721	68	23	and	and	CCONJ
ejpam-4721	68	24	p3p11	p3p11	ADJ
ejpam-4721	68	25	intersect	intersect	ADJ
ejpam-4721	68	26	each	each	DET
ejpam-4721	68	27	other	other	ADJ
ejpam-4721	68	28	at	at	ADP
ejpam-4721	68	29	one	one	NUM
ejpam-4721	68	30	point	point	NOUN
ejpam-4721	68	31	.	.	PUNCT
ejpam-4721	69	1	let	let	VERB
ejpam-4721	69	2	’s	’s	PRON
ejpam-4721	69	3	verify	verify	VERB
ejpam-4721	69	4	this	this	PRON
ejpam-4721	69	5	by	by	ADP
ejpam-4721	69	6	the	the	DET
ejpam-4721	69	7	above	above	PROPN
ejpam-4721	69	8	ceva	ceva	PROPN
ejpam-4721	69	9	’s	’s	PART
ejpam-4721	69	10	theorem	theorem	PROPN
ejpam-4721	69	11	.	.	PUNCT
ejpam-4721	70	1	then	then	ADV
ejpam-4721	70	2	it	it	PRON
ejpam-4721	70	3	is	be	AUX
ejpam-4721	70	4	reduced	reduce	VERB
ejpam-4721	70	5	to	to	ADP
ejpam-4721	70	6	the	the	DET
ejpam-4721	70	7	verification	verification	NOUN
ejpam-4721	70	8	of	of	ADP
ejpam-4721	70	9	the	the	DET
ejpam-4721	70	10	identity	identity	NOUN
ejpam-4721	70	11	sin15	sin15	NOUN
ejpam-4721	70	12	◦	◦	NOUN
ejpam-4721	70	13	sin15	sin15	NOUN
ejpam-4721	70	14	◦	◦	NOUN
ejpam-4721	70	15	·	·	PUNCT
ejpam-4721	70	16	sin30	sin30	NOUN
ejpam-4721	70	17	◦	◦	NOUN
ejpam-4721	70	18	sin15	sin15	NOUN
ejpam-4721	70	19	◦	◦	NOUN
ejpam-4721	70	20	·	·	PUNCT
ejpam-4721	70	21	sin30	sin30	VERB
ejpam-4721	70	22	◦	◦	NOUN
ejpam-4721	70	23	sin75	sin75	NUM
ejpam-4721	70	24	◦	◦	NOUN
ejpam-4721	70	25	=	=	SYM
ejpam-4721	70	26	1	1	NUM
ejpam-4721	70	27	and	and	CCONJ
ejpam-4721	70	28	the	the	DET
ejpam-4721	70	29	validity	validity	NOUN
ejpam-4721	70	30	of	of	ADP
ejpam-4721	70	31	this	this	DET
ejpam-4721	70	32	identity	identity	NOUN
ejpam-4721	70	33	follows	follow	VERB
ejpam-4721	70	34	from	from	ADP
ejpam-4721	70	35	the	the	DET
ejpam-4721	70	36	equalities	equality	NOUN
ejpam-4721	70	37	sin75	sin75	ADP
ejpam-4721	70	38	◦	◦	NOUN
ejpam-4721	70	39	=	=	SYM
ejpam-4721	70	40	cos15	cos15	NOUN
ejpam-4721	70	41	◦	◦	NOUN
ejpam-4721	70	42	,	,	PUNCT
ejpam-4721	70	43	sin30	sin30	VERB
ejpam-4721	70	44	◦	◦	NOUN
ejpam-4721	70	45	=	=	SYM
ejpam-4721	71	1	2sin15	2sin15	NUM
ejpam-4721	71	2	◦	◦	NOUN
ejpam-4721	71	3	cos15	cos15	NOUN
ejpam-4721	71	4	◦	◦	NOUN
ejpam-4721	71	5	.	.	PUNCT
ejpam-4721	72	1	s.	s.	PROPN
ejpam-4721	72	2	j.aliyev	j.aliyev	PROPN
ejpam-4721	72	3	,	,	PUNCT
ejpam-4721	72	4	m.	m.	PROPN
ejpam-4721	72	5	n.heydarova	n.heydarova	PROPN
ejpam-4721	72	6	,	,	PUNCT
ejpam-4721	72	7	s.	s.	PROPN
ejpam-4721	72	8	m.aghazade	m.aghazade	PROPN
ejpam-4721	72	9	/	/	SYM
ejpam-4721	72	10	eur	eur	PROPN
ejpam-4721	72	11	.	.	PUNCT
ejpam-4721	73	1	j.	j.	PROPN
ejpam-4721	73	2	pure	pure	PROPN
ejpam-4721	73	3	appl	appl	PROPN
ejpam-4721	73	4	.	.	PROPN
ejpam-4721	73	5	math	math	PROPN
ejpam-4721	73	6	,	,	PUNCT
ejpam-4721	73	7	16	16	NUM
ejpam-4721	73	8	(	(	PUNCT
ejpam-4721	73	9	2	2	NUM
ejpam-4721	73	10	)	)	PUNCT
ejpam-4721	73	11	(	(	PUNCT
ejpam-4721	73	12	2023	2023	NUM
ejpam-4721	73	13	)	)	PUNCT
ejpam-4721	73	14	,	,	PUNCT
ejpam-4721	73	15	1110	1110	NUM
ejpam-4721	73	16	-	-	SYM
ejpam-4721	73	17	1117	1117	NUM
ejpam-4721	73	18	1114	1114	NUM
ejpam-4721	73	19	figure	figure	NOUN
ejpam-4721	73	20	4	4	NUM
ejpam-4721	73	21	:	:	PUNCT
ejpam-4721	73	22	(	(	PUNCT
ejpam-4721	73	23	segments	segments	PROPN
ejpam-4721	73	24	aa1	aa1	PROPN
ejpam-4721	73	25	,	,	PUNCT
ejpam-4721	73	26	bb1	bb1	PROPN
ejpam-4721	73	27	and	and	CCONJ
ejpam-4721	73	28	cc1	cc1	NOUN
ejpam-4721	73	29	in	in	ADP
ejpam-4721	73	30	the	the	DET
ejpam-4721	73	31	triangle	triangle	NOUN
ejpam-4721	73	32	abc	abc	PROPN
ejpam-4721	73	33	intersect	intersect	ADJ
ejpam-4721	73	34	each	each	DET
ejpam-4721	73	35	other	other	ADJ
ejpam-4721	73	36	at	at	ADP
ejpam-4721	73	37	one	one	NUM
ejpam-4721	73	38	point	point	NOUN
ejpam-4721	73	39	)	)	PUNCT
ejpam-4721	73	40	figure	figure	NOUN
ejpam-4721	73	41	5	5	NUM
ejpam-4721	73	42	:	:	PUNCT
ejpam-4721	73	43	(	(	PUNCT
ejpam-4721	73	44	triangle	triangle	VERB
ejpam-4721	73	45	abc	abc	PROPN
ejpam-4721	73	46	with	with	ADP
ejpam-4721	73	47	the	the	DET
ejpam-4721	73	48	given	give	VERB
ejpam-4721	73	49	angles	angle	NOUN
ejpam-4721	73	50	)	)	PUNCT
ejpam-4721	73	51	note	note	NOUN
ejpam-4721	73	52	that	that	SCONJ
ejpam-4721	73	53	the	the	DET
ejpam-4721	73	54	presented	present	VERB
ejpam-4721	73	55	method	method	NOUN
ejpam-4721	73	56	can	can	AUX
ejpam-4721	73	57	be	be	AUX
ejpam-4721	73	58	used	use	VERB
ejpam-4721	73	59	to	to	PART
ejpam-4721	73	60	solve	solve	VERB
ejpam-4721	73	61	different	different	ADJ
ejpam-4721	73	62	kinds	kind	NOUN
ejpam-4721	73	63	of	of	ADP
ejpam-4721	73	64	problems	problem	NOUN
ejpam-4721	73	65	,	,	PUNCT
ejpam-4721	73	66	not	not	PART
ejpam-4721	73	67	only	only	ADV
ejpam-4721	73	68	the	the	DET
ejpam-4721	73	69	ones	one	NOUN
ejpam-4721	73	70	mentioned	mention	VERB
ejpam-4721	73	71	above	above	ADV
ejpam-4721	73	72	.	.	PUNCT
ejpam-4721	74	1	let	let	VERB
ejpam-4721	74	2	’s	’s	NOUN
ejpam-4721	74	3	consider	consider	VERB
ejpam-4721	74	4	one	one	NUM
ejpam-4721	74	5	of	of	ADP
ejpam-4721	74	6	such	such	ADJ
ejpam-4721	74	7	problems	problem	NOUN
ejpam-4721	74	8	.	.	PUNCT
ejpam-4721	75	1	problem	problem	NOUN
ejpam-4721	75	2	3	3	NUM
ejpam-4721	75	3	.	.	PUNCT
ejpam-4721	76	1	the	the	DET
ejpam-4721	76	2	points	point	NOUN
ejpam-4721	76	3	d	d	NOUN
ejpam-4721	76	4	and	and	CCONJ
ejpam-4721	76	5	e	e	PROPN
ejpam-4721	76	6	are	be	AUX
ejpam-4721	76	7	given	give	VERB
ejpam-4721	76	8	on	on	ADP
ejpam-4721	76	9	the	the	DET
ejpam-4721	76	10	sides	side	NOUN
ejpam-4721	76	11	ab	ab	PROPN
ejpam-4721	76	12	and	and	CCONJ
ejpam-4721	76	13	ac	ac	PROPN
ejpam-4721	76	14	of	of	ADP
ejpam-4721	76	15	the	the	DET
ejpam-4721	76	16	triangle	triangle	NOUN
ejpam-4721	76	17	abc	abc	PROPN
ejpam-4721	76	18	,	,	PUNCT
ejpam-4721	76	19	respectively	respectively	ADV
ejpam-4721	76	20	,	,	PUNCT
ejpam-4721	76	21	so	so	SCONJ
ejpam-4721	76	22	that	that	SCONJ
ejpam-4721	76	23	∠abe	∠abe	PROPN
ejpam-4721	76	24	=	=	SYM
ejpam-4721	76	25	∠cbe	∠cbe	PROPN
ejpam-4721	76	26	=	=	SYM
ejpam-4721	76	27	20	20	NUM
ejpam-4721	76	28	◦	◦	NOUN
ejpam-4721	76	29	,∠acd	,∠acd	PUNCT
ejpam-4721	76	30	=	=	SYM
ejpam-4721	76	31	30	30	NUM
ejpam-4721	76	32	◦	◦	NOUN
ejpam-4721	76	33	,∠bcd	,∠bcd	PUNCT
ejpam-4721	76	34	=	=	SYM
ejpam-4721	76	35	70	70	NUM
ejpam-4721	76	36	◦	◦	NOUN
ejpam-4721	76	37	(	(	PUNCT
ejpam-4721	76	38	fig.7	fig.7	ADJ
ejpam-4721	76	39	)	)	PUNCT
ejpam-4721	76	40	.	.	PUNCT
ejpam-4721	77	1	prove	prove	VERB
ejpam-4721	77	2	that	that	SCONJ
ejpam-4721	77	3	∠bed	∠be	VERB
ejpam-4721	77	4	=	=	SYM
ejpam-4721	77	5	60	60	NUM
ejpam-4721	77	6	◦	◦	NOUN
ejpam-4721	77	7	.	.	PUNCT
ejpam-4721	78	1	as	as	SCONJ
ejpam-4721	78	2	the	the	DET
ejpam-4721	78	3	angles	angle	NOUN
ejpam-4721	78	4	given	give	VERB
ejpam-4721	78	5	in	in	ADP
ejpam-4721	78	6	this	this	DET
ejpam-4721	78	7	problem	problem	NOUN
ejpam-4721	78	8	are	be	AUX
ejpam-4721	78	9	the	the	DET
ejpam-4721	78	10	multiples	multiple	NOUN
ejpam-4721	78	11	of	of	ADP
ejpam-4721	78	12	10	10	NUM
ejpam-4721	78	13	◦	◦	NOUN
ejpam-4721	78	14	,	,	PUNCT
ejpam-4721	78	15	we	we	PRON
ejpam-4721	78	16	divide	divide	VERB
ejpam-4721	78	17	the	the	DET
ejpam-4721	78	18	circle	circle	NOUN
ejpam-4721	78	19	into	into	ADP
ejpam-4721	78	20	18	18	NUM
ejpam-4721	78	21	equal	equal	ADJ
ejpam-4721	78	22	parts	part	NOUN
ejpam-4721	78	23	.	.	PUNCT
ejpam-4721	79	1	if	if	SCONJ
ejpam-4721	79	2	we	we	PRON
ejpam-4721	79	3	place	place	VERB
ejpam-4721	79	4	the	the	DET
ejpam-4721	79	5	triangle	triangle	NOUN
ejpam-4721	79	6	abc	abc	PROPN
ejpam-4721	79	7	inside	inside	ADP
ejpam-4721	79	8	the	the	DET
ejpam-4721	79	9	circle	circle	NOUN
ejpam-4721	79	10	as	as	SCONJ
ejpam-4721	79	11	shown	show	VERB
ejpam-4721	79	12	on	on	ADP
ejpam-4721	79	13	fig.8	fig.8	PROPN
ejpam-4721	79	14	(	(	PUNCT
ejpam-4721	79	15	b	b	PROPN
ejpam-4721	79	16	≡	≡	PROPN
ejpam-4721	79	17	c11	c11	NOUN
ejpam-4721	79	18	,	,	PUNCT
ejpam-4721	79	19	c	c	PROPN
ejpam-4721	79	20	≡	≡	PROPN
ejpam-4721	79	21	c5	c5	PROPN
ejpam-4721	79	22	,	,	PUNCT
ejpam-4721	79	23	e	e	PROPN
ejpam-4721	79	24	≡	≡	PROPN
ejpam-4721	79	25	c3	c3	PROPN
ejpam-4721	79	26	)	)	PUNCT
ejpam-4721	79	27	,	,	PUNCT
ejpam-4721	79	28	then	then	ADV
ejpam-4721	79	29	the	the	DET
ejpam-4721	79	30	conditions	condition	NOUN
ejpam-4721	79	31	of	of	ADP
ejpam-4721	79	32	the	the	DET
ejpam-4721	79	33	problem	problem	NOUN
ejpam-4721	79	34	are	be	AUX
ejpam-4721	79	35	satisfied	satisfied	ADJ
ejpam-4721	79	36	:	:	PUNCT
ejpam-4721	79	37	∠ac11c3	∠ac11c3	ADJ
ejpam-4721	79	38	=	=	SYM
ejpam-4721	79	39	∠c3c11c5	∠c3c11c5	X
ejpam-4721	79	40	=	=	SYM
ejpam-4721	79	41	20	20	NUM
ejpam-4721	79	42	◦	◦	NOUN
ejpam-4721	79	43	,	,	PUNCT
ejpam-4721	79	44	vac5c18	vac5c18	NOUN
ejpam-4721	79	45	=	=	SYM
ejpam-4721	79	46	30	30	NUM
ejpam-4721	79	47	◦	◦	NOUN
ejpam-4721	79	48	,∠c18c5c11	,∠c18c5c11	PUNCT
ejpam-4721	79	49	=	=	SYM
ejpam-4721	79	50	70	70	NUM
ejpam-4721	79	51	◦	◦	NOUN
ejpam-4721	79	52	.	.	PUNCT
ejpam-4721	80	1	from	from	ADP
ejpam-4721	80	2	fig.8	fig.8	PROPN
ejpam-4721	80	3	we	we	PRON
ejpam-4721	80	4	can	can	AUX
ejpam-4721	80	5	see	see	VERB
ejpam-4721	80	6	that	that	SCONJ
ejpam-4721	80	7	the	the	DET
ejpam-4721	80	8	sought	seek	VERB
ejpam-4721	80	9	angle	angle	NOUN
ejpam-4721	80	10	c17c3c11	c17c3c11	PROPN
ejpam-4721	80	11	is	be	AUX
ejpam-4721	80	12	equal	equal	ADJ
ejpam-4721	80	13	to	to	ADP
ejpam-4721	80	14	60	60	NUM
ejpam-4721	80	15	◦	◦	NOUN
ejpam-4721	80	16	.	.	PUNCT
ejpam-4721	81	1	as	as	ADP
ejpam-4721	81	2	for	for	ADP
ejpam-4721	81	3	problem	problem	NOUN
ejpam-4721	81	4	3	3	NUM
ejpam-4721	81	5	,	,	PUNCT
ejpam-4721	81	6	it	it	PRON
ejpam-4721	81	7	is	be	AUX
ejpam-4721	81	8	equivalent	equivalent	ADJ
ejpam-4721	81	9	to	to	ADP
ejpam-4721	81	10	the	the	DET
ejpam-4721	81	11	following	follow	VERB
ejpam-4721	81	12	statement	statement	NOUN
ejpam-4721	81	13	:	:	PUNCT
ejpam-4721	81	14	in	in	ADP
ejpam-4721	81	15	the	the	DET
ejpam-4721	81	16	regular	regular	ADJ
ejpam-4721	81	17	octadecagon	octadecagon	NOUN
ejpam-4721	81	18	,	,	PUNCT
ejpam-4721	81	19	the	the	DET
ejpam-4721	81	20	diagonals	diagonal	NOUN
ejpam-4721	81	21	c1c11	c1c11	PROPN
ejpam-4721	81	22	,	,	PUNCT
ejpam-4721	81	23	c3c17	c3c17	NOUN
ejpam-4721	81	24	and	and	CCONJ
ejpam-4721	81	25	c5c18	c5c18	NOUN
ejpam-4721	81	26	intersect	intersect	ADJ
ejpam-4721	81	27	each	each	DET
ejpam-4721	81	28	other	other	ADJ
ejpam-4721	81	29	at	at	ADP
ejpam-4721	81	30	one	one	NUM
ejpam-4721	81	31	point	point	NOUN
ejpam-4721	81	32	.	.	PUNCT
ejpam-4721	82	1	let	let	VERB
ejpam-4721	82	2	’s	’s	PROPN
ejpam-4721	82	3	s.	s.	PROPN
ejpam-4721	82	4	j.aliyev	j.aliyev	PROPN
ejpam-4721	82	5	,	,	PUNCT
ejpam-4721	82	6	m.	m.	PROPN
ejpam-4721	82	7	n.heydarova	n.heydarova	PROPN
ejpam-4721	82	8	,	,	PUNCT
ejpam-4721	82	9	s.	s.	PROPN
ejpam-4721	82	10	m.aghazade	m.aghazade	PROPN
ejpam-4721	82	11	/	/	SYM
ejpam-4721	82	12	eur	eur	PROPN
ejpam-4721	82	13	.	.	PUNCT
ejpam-4721	83	1	j.	j.	PROPN
ejpam-4721	83	2	pure	pure	PROPN
ejpam-4721	83	3	appl	appl	PROPN
ejpam-4721	83	4	.	.	PROPN
ejpam-4721	83	5	math	math	PROPN
ejpam-4721	83	6	,	,	PUNCT
ejpam-4721	83	7	16	16	NUM
ejpam-4721	83	8	(	(	PUNCT
ejpam-4721	83	9	2	2	NUM
ejpam-4721	83	10	)	)	PUNCT
ejpam-4721	83	11	(	(	PUNCT
ejpam-4721	83	12	2023	2023	NUM
ejpam-4721	83	13	)	)	PUNCT
ejpam-4721	83	14	,	,	PUNCT
ejpam-4721	83	15	1110	1110	NUM
ejpam-4721	83	16	-	-	SYM
ejpam-4721	83	17	1117	1117	NUM
ejpam-4721	83	18	1115	1115	NUM
ejpam-4721	83	19	figure	figure	NOUN
ejpam-4721	83	20	6	6	NUM
ejpam-4721	83	21	:	:	PUNCT
ejpam-4721	83	22	(	(	PUNCT
ejpam-4721	83	23	triangle	triangle	NOUN
ejpam-4721	83	24	p1p10p3	p1p10p3	VERB
ejpam-4721	83	25	,	,	PUNCT
ejpam-4721	83	26	equal	equal	ADJ
ejpam-4721	83	27	to	to	PART
ejpam-4721	83	28	triangle	triangle	VERB
ejpam-4721	83	29	abc	abc	PROPN
ejpam-4721	83	30	,	,	PUNCT
ejpam-4721	83	31	placed	place	VERB
ejpam-4721	83	32	inside	inside	ADP
ejpam-4721	83	33	the	the	DET
ejpam-4721	83	34	circle	circle	NOUN
ejpam-4721	83	35	)	)	PUNCT
ejpam-4721	83	36	prove	prove	VERB
ejpam-4721	83	37	this	this	DET
ejpam-4721	83	38	statement	statement	NOUN
ejpam-4721	83	39	as	as	SCONJ
ejpam-4721	83	40	follows	follow	VERB
ejpam-4721	83	41	.	.	PUNCT
ejpam-4721	84	1	it	it	PRON
ejpam-4721	84	2	suffices	suffice	VERB
ejpam-4721	84	3	to	to	PART
ejpam-4721	84	4	show	show	VERB
ejpam-4721	84	5	that	that	SCONJ
ejpam-4721	84	6	∠c17dc18	∠c17dc18	PROPN
ejpam-4721	84	7	+	+	CCONJ
ejpam-4721	84	8	∠c18dc1	∠c18dc1	X
ejpam-4721	85	1	+	+	CCONJ
ejpam-4721	85	2	∠c1dc3	∠c1dc3	X
ejpam-4721	85	3	=	=	NOUN
ejpam-4721	85	4	180	180	NUM
ejpam-4721	85	5	◦	◦	NOUN
ejpam-4721	85	6	.	.	PUNCT
ejpam-4721	86	1	indeed	indeed	ADV
ejpam-4721	86	2	,	,	PUNCT
ejpam-4721	86	3	∠c17dc18	∠c17dc18	PROPN
ejpam-4721	86	4	=	=	SYM
ejpam-4721	86	5	1	1	NUM
ejpam-4721	86	6	2	2	NUM
ejpam-4721	86	7	(	(	PUNCT
ejpam-4721	86	8	∪c17c18	∪c17c18	NOUN
ejpam-4721	86	9	+	+	CCONJ
ejpam-4721	86	10	∪c3c5	∪c3c5	NUM
ejpam-4721	86	11	)	)	PUNCT
ejpam-4721	86	12	=	=	SYM
ejpam-4721	86	13	10	10	NUM
ejpam-4721	86	14	◦	◦	NOUN
ejpam-4721	86	15	+	+	NUM
ejpam-4721	86	16	20	20	NUM
ejpam-4721	86	17	◦	◦	NOUN
ejpam-4721	86	18	=	=	SYM
ejpam-4721	86	19	30	30	NUM
ejpam-4721	86	20	◦	◦	NOUN
ejpam-4721	86	21	,	,	PUNCT
ejpam-4721	86	22	∠c18dc1	∠c18dc1	X
ejpam-4721	86	23	=	=	SYM
ejpam-4721	86	24	1	1	NUM
ejpam-4721	86	25	2	2	NUM
ejpam-4721	86	26	(	(	PUNCT
ejpam-4721	86	27	∪c1c18	∪c1c18	NOUN
ejpam-4721	86	28	+	+	CCONJ
ejpam-4721	86	29	∪c5c11	∪c5c11	X
ejpam-4721	86	30	)	)	PUNCT
ejpam-4721	86	31	=	=	SYM
ejpam-4721	86	32	10	10	NUM
ejpam-4721	86	33	◦	◦	NOUN
ejpam-4721	86	34	+	+	CCONJ
ejpam-4721	86	35	60	60	NUM
ejpam-4721	86	36	◦	◦	NOUN
ejpam-4721	86	37	=	=	SYM
ejpam-4721	86	38	70	70	NUM
ejpam-4721	86	39	◦	◦	NOUN
ejpam-4721	86	40	,	,	PUNCT
ejpam-4721	86	41	∠c1dc3	∠c1dc3	PROPN
ejpam-4721	86	42	=	=	NOUN
ejpam-4721	86	43	1	1	NUM
ejpam-4721	86	44	2	2	NUM
ejpam-4721	86	45	(	(	PUNCT
ejpam-4721	86	46	∪c1c3	∪c1c3	X
ejpam-4721	86	47	+	+	NUM
ejpam-4721	86	48	∪c11c17	∪c11c17	NOUN
ejpam-4721	86	49	)	)	PUNCT
ejpam-4721	86	50	=	=	SYM
ejpam-4721	86	51	20	20	NUM
ejpam-4721	86	52	◦	◦	NOUN
ejpam-4721	86	53	+	+	CCONJ
ejpam-4721	86	54	60	60	NUM
ejpam-4721	86	55	◦	◦	NOUN
ejpam-4721	86	56	=	=	SYM
ejpam-4721	86	57	80	80	NUM
ejpam-4721	86	58	◦	◦	NOUN
ejpam-4721	86	59	,	,	PUNCT
ejpam-4721	86	60	figure	figure	VERB
ejpam-4721	86	61	7	7	NUM
ejpam-4721	86	62	:	:	PUNCT
ejpam-4721	86	63	(	(	PUNCT
ejpam-4721	86	64	triangle	triangle	VERB
ejpam-4721	86	65	abc	abc	PROPN
ejpam-4721	86	66	with	with	ADP
ejpam-4721	86	67	the	the	DET
ejpam-4721	86	68	given	give	VERB
ejpam-4721	86	69	angles	angle	NOUN
ejpam-4721	86	70	)	)	PUNCT
ejpam-4721	86	71	references	reference	NOUN
ejpam-4721	86	72	1116	1116	NUM
ejpam-4721	86	73	figure	figure	NOUN
ejpam-4721	86	74	8	8	NUM
ejpam-4721	86	75	:	:	PUNCT
ejpam-4721	86	76	(	(	PUNCT
ejpam-4721	86	77	triangle	triangle	NOUN
ejpam-4721	86	78	ac11c3	ac11c3	PROPN
ejpam-4721	86	79	,	,	PUNCT
ejpam-4721	86	80	equal	equal	ADJ
ejpam-4721	86	81	to	to	PART
ejpam-4721	86	82	triangle	triangle	VERB
ejpam-4721	86	83	abc	abc	PROPN
ejpam-4721	86	84	,	,	PUNCT
ejpam-4721	86	85	placed	place	VERB
ejpam-4721	86	86	inside	inside	ADP
ejpam-4721	86	87	the	the	DET
ejpam-4721	86	88	circle	circle	NOUN
ejpam-4721	86	89	)	)	PUNCT
ejpam-4721	86	90	3	3	X
ejpam-4721	86	91	.	.	X
ejpam-4721	86	92	concluding	conclude	VERB
ejpam-4721	86	93	remarks	remark	NOUN
ejpam-4721	86	94	this	this	DET
ejpam-4721	86	95	work	work	NOUN
ejpam-4721	86	96	deals	deal	NOUN
ejpam-4721	86	97	with	with	ADP
ejpam-4721	86	98	the	the	DET
ejpam-4721	86	99	solution	solution	NOUN
ejpam-4721	86	100	of	of	ADP
ejpam-4721	86	101	integer	integer	NOUN
ejpam-4721	86	102	angled	angle	VERB
ejpam-4721	86	103	triangle	triangle	NOUN
ejpam-4721	86	104	problems	problem	NOUN
ejpam-4721	86	105	in	in	ADP
ejpam-4721	86	106	geometry	geometry	NOUN
ejpam-4721	86	107	.	.	PUNCT
ejpam-4721	87	1	usually	usually	ADV
ejpam-4721	87	2	,	,	PUNCT
ejpam-4721	87	3	these	these	DET
ejpam-4721	87	4	problems	problem	NOUN
ejpam-4721	87	5	are	be	AUX
ejpam-4721	87	6	solved	solve	VERB
ejpam-4721	87	7	by	by	ADP
ejpam-4721	87	8	the	the	DET
ejpam-4721	87	9	method	method	NOUN
ejpam-4721	87	10	of	of	ADP
ejpam-4721	87	11	additional	additional	ADJ
ejpam-4721	87	12	constructions	construction	NOUN
ejpam-4721	87	13	,	,	PUNCT
ejpam-4721	87	14	which	which	PRON
ejpam-4721	87	15	requires	require	VERB
ejpam-4721	87	16	a	a	DET
ejpam-4721	87	17	lot	lot	NOUN
ejpam-4721	87	18	of	of	ADP
ejpam-4721	87	19	experience	experience	NOUN
ejpam-4721	87	20	and	and	CCONJ
ejpam-4721	87	21	geometric	geometric	ADJ
ejpam-4721	87	22	intuition	intuition	NOUN
ejpam-4721	87	23	as	as	SCONJ
ejpam-4721	87	24	there	there	PRON
ejpam-4721	87	25	is	be	VERB
ejpam-4721	87	26	no	no	DET
ejpam-4721	87	27	general	general	ADJ
ejpam-4721	87	28	algorithm	algorithm	NOUN
ejpam-4721	87	29	for	for	ADP
ejpam-4721	87	30	solving	solve	VERB
ejpam-4721	87	31	problems	problem	NOUN
ejpam-4721	87	32	by	by	ADP
ejpam-4721	87	33	this	this	DET
ejpam-4721	87	34	method	method	NOUN
ejpam-4721	87	35	.	.	PUNCT
ejpam-4721	88	1	in	in	ADP
ejpam-4721	88	2	this	this	DET
ejpam-4721	88	3	work	work	NOUN
ejpam-4721	88	4	,	,	PUNCT
ejpam-4721	88	5	we	we	PRON
ejpam-4721	88	6	present	present	VERB
ejpam-4721	88	7	the	the	DET
ejpam-4721	88	8	method	method	NOUN
ejpam-4721	88	9	of	of	ADP
ejpam-4721	88	10	auxiliary	auxiliary	ADJ
ejpam-4721	88	11	circle	circle	NOUN
ejpam-4721	88	12	divided	divide	VERB
ejpam-4721	88	13	into	into	ADP
ejpam-4721	88	14	equal	equal	ADJ
ejpam-4721	88	15	parts	part	NOUN
ejpam-4721	88	16	,	,	PUNCT
ejpam-4721	88	17	justification	justification	NOUN
ejpam-4721	88	18	of	of	ADP
ejpam-4721	88	19	which	which	PRON
ejpam-4721	88	20	is	be	AUX
ejpam-4721	88	21	based	base	VERB
ejpam-4721	88	22	on	on	ADP
ejpam-4721	88	23	one	one	NUM
ejpam-4721	88	24	property	property	NOUN
ejpam-4721	88	25	of	of	ADP
ejpam-4721	88	26	diagonals	diagonal	NOUN
ejpam-4721	88	27	of	of	ADP
ejpam-4721	88	28	regular	regular	ADJ
ejpam-4721	88	29	polygons	polygon	NOUN
ejpam-4721	88	30	:	:	PUNCT
ejpam-4721	88	31	three	three	NUM
ejpam-4721	88	32	diagonals	diagonal	NOUN
ejpam-4721	88	33	in	in	ADP
ejpam-4721	88	34	regular	regular	ADJ
ejpam-4721	88	35	polygons	polygon	NOUN
ejpam-4721	88	36	intersect	intersect	ADJ
ejpam-4721	88	37	each	each	DET
ejpam-4721	88	38	other	other	ADJ
ejpam-4721	88	39	at	at	ADP
ejpam-4721	88	40	one	one	NUM
ejpam-4721	88	41	point	point	NOUN
ejpam-4721	88	42	.	.	PUNCT
ejpam-4721	89	1	from	from	ADP
ejpam-4721	89	2	the	the	DET
ejpam-4721	89	3	problems	problem	NOUN
ejpam-4721	89	4	solved	solve	VERB
ejpam-4721	89	5	above	above	ADP
ejpam-4721	89	6	it	it	PRON
ejpam-4721	89	7	can	can	AUX
ejpam-4721	89	8	be	be	AUX
ejpam-4721	89	9	seen	see	VERB
ejpam-4721	89	10	that	that	SCONJ
ejpam-4721	89	11	our	our	PRON
ejpam-4721	89	12	method	method	NOUN
ejpam-4721	89	13	is	be	AUX
ejpam-4721	89	14	simple	simple	ADJ
ejpam-4721	89	15	and	and	CCONJ
ejpam-4721	89	16	easy	easy	ADJ
ejpam-4721	89	17	.	.	PUNCT
ejpam-4721	90	1	references	reference	NOUN
ejpam-4721	90	2	[	[	X
ejpam-4721	90	3	1	1	X
ejpam-4721	90	4	]	]	PUNCT
ejpam-4721	90	5	s.	s.	PROPN
ejpam-4721	90	6	aliyev	aliyev	PROPN
ejpam-4721	90	7	,	,	PUNCT
ejpam-4721	90	8	sh	sh	PROPN
ejpam-4721	90	9	.	.	PROPN
ejpam-4721	90	10	aghazade	aghazade	PROPN
ejpam-4721	90	11	,	,	PUNCT
ejpam-4721	90	12	and	and	CCONJ
ejpam-4721	90	13	g.	g.	PROPN
ejpam-4721	90	14	abdullayeva	abdullayeva	PROPN
ejpam-4721	90	15	.	.	PUNCT
ejpam-4721	91	1	using	use	VERB
ejpam-4721	91	2	area	area	NOUN
ejpam-4721	91	3	method	method	NOUN
ejpam-4721	91	4	in	in	ADP
ejpam-4721	91	5	secondary	secondary	ADJ
ejpam-4721	91	6	school	school	NOUN
ejpam-4721	91	7	geometry	geometry	NOUN
ejpam-4721	91	8	.	.	PUNCT
ejpam-4721	92	1	european	european	PROPN
ejpam-4721	92	2	journal	journal	PROPN
ejpam-4721	92	3	of	of	ADP
ejpam-4721	92	4	pure	pure	ADJ
ejpam-4721	92	5	and	and	CCONJ
ejpam-4721	92	6	applied	applied	ADJ
ejpam-4721	92	7	mathematics	mathematic	NOUN
ejpam-4721	92	8	,	,	PUNCT
ejpam-4721	92	9	14(2):601–607	14(2):601–607	PROPN
ejpam-4721	92	10	,	,	PUNCT
ejpam-4721	92	11	2021	2021	NUM
ejpam-4721	92	12	.	.	PUNCT
ejpam-4721	93	1	[	[	X
ejpam-4721	93	2	2	2	NUM
ejpam-4721	93	3	]	]	PUNCT
ejpam-4721	93	4	s.	s.	PROPN
ejpam-4721	93	5	aliyev	aliyev	PROPN
ejpam-4721	93	6	,	,	PUNCT
ejpam-4721	93	7	sh	sh	PROPN
ejpam-4721	93	8	.	.	PROPN
ejpam-4721	93	9	hamidova	hamidova	PROPN
ejpam-4721	93	10	,	,	PUNCT
ejpam-4721	93	11	and	and	CCONJ
ejpam-4721	93	12	g.	g.	PROPN
ejpam-4721	93	13	abdullayeva	abdullayeva	PROPN
ejpam-4721	93	14	.	.	PUNCT
ejpam-4721	94	1	some	some	DET
ejpam-4721	94	2	applications	application	NOUN
ejpam-4721	94	3	of	of	ADP
ejpam-4721	94	4	ptolemy	ptolemy	PROPN
ejpam-4721	94	5	’s	’s	PART
ejpam-4721	94	6	theorem	theorem	NOUN
ejpam-4721	94	7	in	in	ADP
ejpam-4721	94	8	secondary	secondary	ADJ
ejpam-4721	94	9	school	school	NOUN
ejpam-4721	94	10	mathematics	mathematic	NOUN
ejpam-4721	94	11	.	.	PUNCT
ejpam-4721	95	1	european	european	PROPN
ejpam-4721	95	2	journal	journal	PROPN
ejpam-4721	95	3	of	of	ADP
ejpam-4721	95	4	pure	pure	ADJ
ejpam-4721	95	5	and	and	CCONJ
ejpam-4721	95	6	applied	applied	ADJ
ejpam-4721	95	7	mathematics	mathematic	NOUN
ejpam-4721	95	8	,	,	PUNCT
ejpam-4721	95	9	13(1):180–184	13(1):180–184	PROPN
ejpam-4721	95	10	,	,	PUNCT
ejpam-4721	95	11	2020	2020	NUM
ejpam-4721	95	12	.	.	PUNCT
ejpam-4721	96	1	[	[	X
ejpam-4721	96	2	3	3	X
ejpam-4721	96	3	]	]	X
ejpam-4721	96	4	s.	s.	PROPN
ejpam-4721	96	5	krackov	krackov	PROPN
ejpam-4721	96	6	.	.	PUNCT
ejpam-4721	97	1	multivariate	multivariate	PROPN
ejpam-4721	97	2	visual	visual	ADJ
ejpam-4721	97	3	-	-	PUNCT
ejpam-4721	97	4	graphic	graphic	ADJ
ejpam-4721	97	5	representation	representation	NOUN
ejpam-4721	97	6	of	of	ADP
ejpam-4721	97	7	mathematical	mathematical	ADJ
ejpam-4721	97	8	problems	problem	NOUN
ejpam-4721	97	9	.	.	PUNCT
ejpam-4721	98	1	mathematika	mathematika	PROPN
ejpam-4721	98	2	v	v	PROPN
ejpam-4721	98	3	şkole	şkole	PROPN
ejpam-4721	98	4	,	,	PUNCT
ejpam-4721	98	5	(	(	PUNCT
ejpam-4721	98	6	1	1	NUM
ejpam-4721	98	7	)	)	PUNCT
ejpam-4721	98	8	,	,	PUNCT
ejpam-4721	98	9	2013	2013	NUM
ejpam-4721	98	10	.	.	PUNCT
ejpam-4721	99	1	(	(	PUNCT
ejpam-4721	99	2	in	in	ADP
ejpam-4721	99	3	russian	russian	NOUN
ejpam-4721	99	4	)	)	PUNCT
ejpam-4721	99	5	.	.	PUNCT
ejpam-4721	100	1	references	reference	NOUN
ejpam-4721	100	2	1117	1117	NUM
ejpam-4721	100	3	[	[	X
ejpam-4721	100	4	4	4	NUM
ejpam-4721	100	5	]	]	X
ejpam-4721	100	6	y.p	y.p	PROPN
ejpam-4721	100	7	.	.	PROPN
ejpam-4721	100	8	ponarin	ponarin	PROPN
ejpam-4721	100	9	.	.	PUNCT
ejpam-4721	101	1	elementary	elementary	ADJ
ejpam-4721	101	2	geometry	geometry	PROPN
ejpam-4721	101	3	.	.	PUNCT
ejpam-4721	102	1	mtsnmo	mtsnmo	PROPN
ejpam-4721	102	2	,	,	PUNCT
ejpam-4721	102	3	moscow	moscow	PROPN
ejpam-4721	102	4	,	,	PUNCT
ejpam-4721	102	5	2008	2008	NUM
ejpam-4721	102	6	.	.	PUNCT
ejpam-4721	103	1	(	(	PUNCT
ejpam-4721	103	2	in	in	ADP
ejpam-4721	103	3	russian	russian	NOUN
ejpam-4721	103	4	)	)	PUNCT
ejpam-4721	103	5	.	.	PUNCT
ejpam-4721	104	1	[	[	X
ejpam-4721	104	2	5	5	X
ejpam-4721	104	3	]	]	PUNCT
ejpam-4721	104	4	michael	michael	PROPN
ejpam-4721	104	5	serra	serra	PROPN
ejpam-4721	104	6	.	.	PUNCT
ejpam-4721	104	7	discovering	discover	VERB
ejpam-4721	104	8	geometry	geometry	NOUN
ejpam-4721	104	9	an	an	DET
ejpam-4721	104	10	investigative	investigative	ADJ
ejpam-4721	104	11	approach	approach	NOUN
ejpam-4721	104	12	.	.	PUNCT
ejpam-4721	105	1	key	key	ADJ
ejpam-4721	105	2	curriculum	curriculum	PROPN
ejpam-4721	105	3	press	press	NOUN
ejpam-4721	105	4	,	,	PUNCT
ejpam-4721	105	5	2003	2003	NUM
ejpam-4721	105	6	.	.	PUNCT
ejpam-4721	106	1	[	[	X
ejpam-4721	106	2	6	6	NUM
ejpam-4721	106	3	]	]	SYM
ejpam-4721	106	4	i.f	i.f	PROPN
ejpam-4721	106	5	.	.	PROPN
ejpam-4721	106	6	sharigin	sharigin	PROPN
ejpam-4721	106	7	.	.	PUNCT
ejpam-4721	107	1	geometry	geometry	NOUN
ejpam-4721	107	2	.	.	PUNCT
ejpam-4721	108	1	drofa	drofa	NOUN
ejpam-4721	108	2	,	,	PUNCT
ejpam-4721	108	3	m.	m.	NOUN
ejpam-4721	108	4	,	,	PUNCT
ejpam-4721	108	5	1999	1999	NUM
ejpam-4721	108	6	.	.	PUNCT
ejpam-4721	109	1	(	(	PUNCT
ejpam-4721	109	2	in	in	ADP
ejpam-4721	109	3	russian	russian	NOUN
ejpam-4721	109	4	)	)	PUNCT
ejpam-4721	109	5	.	.	PUNCT
ejpam-4721	110	1	[	[	X
ejpam-4721	110	2	7	7	NUM
ejpam-4721	110	3	]	]	X
ejpam-4721	110	4	hung	hung	PROPN
ejpam-4721	110	5	-	-	PUNCT
ejpam-4721	110	6	hsi	hsi	PROPN
ejpam-4721	110	7	wu	wu	PROPN
ejpam-4721	110	8	.	.	PUNCT
ejpam-4721	111	1	teaching	teach	VERB
ejpam-4721	111	2	geometry	geometry	NOUN
ejpam-4721	111	3	in	in	ADP
ejpam-4721	111	4	grade	grade	NOUN
ejpam-4721	111	5	8	8	NUM
ejpam-4721	111	6	and	and	CCONJ
ejpam-4721	111	7	high	high	ADJ
ejpam-4721	111	8	school	school	NOUN
ejpam-4721	111	9	according	accord	VERB
ejpam-4721	111	10	to	to	ADP
ejpam-4721	111	11	the	the	DET
ejpam-4721	111	12	common	common	ADJ
ejpam-4721	111	13	core	core	NOUN
ejpam-4721	111	14	standards	standard	NOUN
ejpam-4721	111	15	.	.	PUNCT
ejpam-4721	112	1	2013	2013	NUM
ejpam-4721	112	2	.	.	PUNCT
ejpam-4721	113	1	october	october	PROPN
ejpam-4721	113	2	16	16	NUM
ejpam-4721	113	3	,	,	PUNCT
ejpam-4721	113	4	2021	2021	NUM
ejpam-4721	113	5	,	,	PUNCT
ejpam-4721	113	6	202	202	NUM
ejpam-4721	114	1	p.	p.	NOUN