id	sid	tid	token	lemma	pos
ejpam-3942	1	1	european	european	PROPN
ejpam-3942	1	2	journal	journal	PROPN
ejpam-3942	1	3	of	of	ADP
ejpam-3942	1	4	pure	pure	ADJ
ejpam-3942	1	5	and	and	CCONJ
ejpam-3942	1	6	applied	apply	VERB
ejpam-3942	1	7	mathematics	mathematic	NOUN
ejpam-3942	1	8	vol	vol	NOUN
ejpam-3942	1	9	.	.	PUNCT
ejpam-3942	2	1	14	14	NUM
ejpam-3942	2	2	,	,	PUNCT
ejpam-3942	2	3	no	no	INTJ
ejpam-3942	2	4	.	.	NOUN
ejpam-3942	2	5	2	2	NUM
ejpam-3942	2	6	,	,	PUNCT
ejpam-3942	2	7	2021	2021	NUM
ejpam-3942	2	8	,	,	PUNCT
ejpam-3942	2	9	601	601	NUM
ejpam-3942	2	10	-	-	SYM
ejpam-3942	2	11	607	607	NUM
ejpam-3942	2	12	issn	issn	PROPN
ejpam-3942	2	13	1307	1307	NUM
ejpam-3942	2	14	-	-	SYM
ejpam-3942	2	15	5543	5543	NUM
ejpam-3942	2	16	–	–	PUNCT
ejpam-3942	3	1	ejpam.com	ejpam.com	X
ejpam-3942	3	2	published	publish	VERB
ejpam-3942	3	3	by	by	ADP
ejpam-3942	3	4	new	new	PROPN
ejpam-3942	3	5	york	york	PROPN
ejpam-3942	3	6	business	business	PROPN
ejpam-3942	3	7	global	global	ADJ
ejpam-3942	3	8	using	use	VERB
ejpam-3942	3	9	area	area	NOUN
ejpam-3942	3	10	method	method	NOUN
ejpam-3942	3	11	in	in	ADP
ejpam-3942	3	12	secondary	secondary	ADJ
ejpam-3942	3	13	school	school	NOUN
ejpam-3942	3	14	geometry	geometry	NOUN
ejpam-3942	3	15	samed	samed	PROPN
ejpam-3942	3	16	j.aliyev1∗	j.aliyev1∗	NOUN
ejpam-3942	3	17	,	,	PUNCT
ejpam-3942	3	18	shahin	shahin	PROPN
ejpam-3942	3	19	m.aghazade1	m.aghazade1	NOUN
ejpam-3942	3	20	,	,	PUNCT
ejpam-3942	3	21	goncha	goncha	PROPN
ejpam-3942	3	22	z.abdullayeva1	z.abdullayeva1	PROPN
ejpam-3942	3	23	1	1	NUM
ejpam-3942	3	24	department	department	NOUN
ejpam-3942	3	25	of	of	ADP
ejpam-3942	3	26	methods	method	NOUN
ejpam-3942	3	27	of	of	ADP
ejpam-3942	3	28	mathematics	mathematic	NOUN
ejpam-3942	3	29	and	and	CCONJ
ejpam-3942	3	30	its	its	PRON
ejpam-3942	3	31	teaching	teaching	NOUN
ejpam-3942	3	32	,	,	PUNCT
ejpam-3942	3	33	faculty	faculty	NOUN
ejpam-3942	3	34	of	of	ADP
ejpam-3942	3	35	mechanics	mechanic	NOUN
ejpam-3942	3	36	and	and	CCONJ
ejpam-3942	3	37	mathematics	mathematic	NOUN
ejpam-3942	3	38	,	,	PUNCT
ejpam-3942	3	39	baku	baku	PROPN
ejpam-3942	3	40	state	state	PROPN
ejpam-3942	3	41	university	university	PROPN
ejpam-3942	3	42	,	,	PUNCT
ejpam-3942	3	43	baku	baku	PROPN
ejpam-3942	3	44	,	,	PUNCT
ejpam-3942	3	45	z.khalilov	z.khalilov	PROPN
ejpam-3942	3	46	str.23	str.23	NOUN
ejpam-3942	3	47	,	,	PUNCT
ejpam-3942	3	48	,	,	PUNCT
ejpam-3942	3	49	az1148	az1148	PROPN
ejpam-3942	3	50	,	,	PUNCT
ejpam-3942	3	51	azerbaijan	azerbaijan	PROPN
ejpam-3942	3	52	abstract	abstract	NOUN
ejpam-3942	3	53	.	.	PUNCT
ejpam-3942	4	1	areas	area	NOUN
ejpam-3942	4	2	are	be	AUX
ejpam-3942	4	3	actively	actively	ADV
ejpam-3942	4	4	used	use	VERB
ejpam-3942	4	5	in	in	ADP
ejpam-3942	4	6	the	the	DET
ejpam-3942	4	7	solution	solution	NOUN
ejpam-3942	4	8	of	of	ADP
ejpam-3942	4	9	many	many	ADJ
ejpam-3942	4	10	geometrical	geometrical	ADJ
ejpam-3942	4	11	problems	problem	NOUN
ejpam-3942	4	12	.	.	PUNCT
ejpam-3942	5	1	in	in	ADP
ejpam-3942	5	2	this	this	DET
ejpam-3942	5	3	work	work	NOUN
ejpam-3942	5	4	,	,	PUNCT
ejpam-3942	5	5	smart	smart	ADJ
ejpam-3942	5	6	and	and	CCONJ
ejpam-3942	5	7	laconic	laconic	ADJ
ejpam-3942	5	8	solutions	solution	NOUN
ejpam-3942	5	9	are	be	AUX
ejpam-3942	5	10	found	find	VERB
ejpam-3942	5	11	for	for	ADP
ejpam-3942	5	12	various	various	ADJ
ejpam-3942	5	13	problems	problem	NOUN
ejpam-3942	5	14	by	by	ADP
ejpam-3942	5	15	means	mean	NOUN
ejpam-3942	5	16	of	of	ADP
ejpam-3942	5	17	the	the	DET
ejpam-3942	5	18	area	area	NOUN
ejpam-3942	5	19	method	method	NOUN
ejpam-3942	5	20	.	.	PUNCT
ejpam-3942	6	1	the	the	DET
ejpam-3942	6	2	well	well	ADV
ejpam-3942	6	3	-	-	PUNCT
ejpam-3942	6	4	known	know	VERB
ejpam-3942	6	5	trigonometric	trigonometric	ADJ
ejpam-3942	6	6	addition	addition	NOUN
ejpam-3942	6	7	formula	formula	NOUN
ejpam-3942	6	8	is	be	AUX
ejpam-3942	6	9	also	also	ADV
ejpam-3942	6	10	proved	prove	VERB
ejpam-3942	6	11	.	.	PUNCT
ejpam-3942	7	1	in	in	ADP
ejpam-3942	7	2	the	the	DET
ejpam-3942	7	3	area	area	NOUN
ejpam-3942	7	4	method	method	NOUN
ejpam-3942	7	5	,	,	PUNCT
ejpam-3942	7	6	the	the	DET
ejpam-3942	7	7	given	give	VERB
ejpam-3942	7	8	formulas	formula	NOUN
ejpam-3942	7	9	are	be	AUX
ejpam-3942	7	10	divided	divide	VERB
ejpam-3942	7	11	into	into	ADP
ejpam-3942	7	12	the	the	DET
ejpam-3942	7	13	parts	part	NOUN
ejpam-3942	7	14	,	,	PUNCT
ejpam-3942	7	15	whose	whose	DET
ejpam-3942	7	16	areas	area	NOUN
ejpam-3942	7	17	are	be	AUX
ejpam-3942	7	18	then	then	ADV
ejpam-3942	7	19	calculated	calculate	VERB
ejpam-3942	7	20	using	use	VERB
ejpam-3942	7	21	problem	problem	NOUN
ejpam-3942	7	22	data	datum	NOUN
ejpam-3942	7	23	.	.	PUNCT
ejpam-3942	8	1	2020	2020	NUM
ejpam-3942	8	2	mathematics	mathematics	PROPN
ejpam-3942	8	3	subject	subject	NOUN
ejpam-3942	8	4	classifications	classification	NOUN
ejpam-3942	8	5	:	:	PUNCT
ejpam-3942	8	6	97g10	97g10	NUM
ejpam-3942	8	7	,	,	PUNCT
ejpam-3942	8	8	97g30	97g30	NUM
ejpam-3942	8	9	,	,	PUNCT
ejpam-3942	8	10	97g40	97g40	NUM
ejpam-3942	8	11	key	key	ADJ
ejpam-3942	8	12	words	word	NOUN
ejpam-3942	8	13	and	and	CCONJ
ejpam-3942	8	14	phrases	phrase	NOUN
ejpam-3942	8	15	:	:	PUNCT
ejpam-3942	8	16	area	area	NOUN
ejpam-3942	8	17	method	method	NOUN
ejpam-3942	8	18	,	,	PUNCT
ejpam-3942	8	19	additive	additive	ADJ
ejpam-3942	8	20	property	property	NOUN
ejpam-3942	8	21	of	of	ADP
ejpam-3942	8	22	area	area	NOUN
ejpam-3942	8	23	,	,	PUNCT
ejpam-3942	8	24	excircles	excircle	NOUN
ejpam-3942	8	25	of	of	ADP
ejpam-3942	8	26	a	a	DET
ejpam-3942	8	27	triangle	triangle	NOUN
ejpam-3942	8	28	,	,	PUNCT
ejpam-3942	8	29	addition	addition	NOUN
ejpam-3942	8	30	formula	formula	NOUN
ejpam-3942	8	31	.	.	PUNCT
ejpam-3942	9	1	overcoming	overcome	VERB
ejpam-3942	9	2	the	the	DET
ejpam-3942	9	3	difficulties	difficulty	NOUN
ejpam-3942	9	4	faced	face	VERB
ejpam-3942	9	5	by	by	ADP
ejpam-3942	9	6	the	the	DET
ejpam-3942	9	7	schoolchildren	schoolchildren	NOUN
ejpam-3942	9	8	in	in	ADP
ejpam-3942	9	9	solving	solve	VERB
ejpam-3942	9	10	geometrical	geometrical	ADJ
ejpam-3942	9	11	problems	problem	NOUN
ejpam-3942	9	12	is	be	AUX
ejpam-3942	9	13	still	still	ADV
ejpam-3942	9	14	actual	actual	ADJ
ejpam-3942	9	15	today	today	NOUN
ejpam-3942	9	16	.	.	PUNCT
ejpam-3942	10	1	including	include	VERB
ejpam-3942	10	2	geometrical	geometrical	ADJ
ejpam-3942	10	3	methods	method	NOUN
ejpam-3942	10	4	of	of	ADP
ejpam-3942	10	5	problem	problem	NOUN
ejpam-3942	10	6	solving	solve	VERB
ejpam-3942	10	7	in	in	ADP
ejpam-3942	10	8	secondary	secondary	ADJ
ejpam-3942	10	9	school	school	NOUN
ejpam-3942	10	10	programs	program	NOUN
ejpam-3942	10	11	is	be	AUX
ejpam-3942	10	12	one	one	NUM
ejpam-3942	10	13	of	of	ADP
ejpam-3942	10	14	the	the	DET
ejpam-3942	10	15	way	way	NOUN
ejpam-3942	10	16	to	to	PART
ejpam-3942	10	17	solve	solve	VERB
ejpam-3942	10	18	this	this	DET
ejpam-3942	10	19	problem	problem	NOUN
ejpam-3942	10	20	within	within	ADP
ejpam-3942	10	21	the	the	DET
ejpam-3942	10	22	concept	concept	NOUN
ejpam-3942	10	23	of	of	ADP
ejpam-3942	10	24	humanitarian	humanitarian	ADJ
ejpam-3942	10	25	school	school	NOUN
ejpam-3942	10	26	education	education	NOUN
ejpam-3942	10	27	.	.	PUNCT
ejpam-3942	11	1	in	in	ADP
ejpam-3942	11	2	this	this	DET
ejpam-3942	11	3	work	work	NOUN
ejpam-3942	11	4	,	,	PUNCT
ejpam-3942	11	5	we	we	PRON
ejpam-3942	11	6	consider	consider	VERB
ejpam-3942	11	7	the	the	DET
ejpam-3942	11	8	importance	importance	NOUN
ejpam-3942	11	9	and	and	CCONJ
ejpam-3942	11	10	the	the	DET
ejpam-3942	11	11	possibility	possibility	NOUN
ejpam-3942	11	12	of	of	ADP
ejpam-3942	11	13	including	include	VERB
ejpam-3942	11	14	the	the	DET
ejpam-3942	11	15	area	area	NOUN
ejpam-3942	11	16	method	method	NOUN
ejpam-3942	11	17	in	in	ADP
ejpam-3942	11	18	secondary	secondary	ADJ
ejpam-3942	11	19	school	school	NOUN
ejpam-3942	11	20	programs	program	NOUN
ejpam-3942	11	21	,	,	PUNCT
ejpam-3942	11	22	which	which	PRON
ejpam-3942	11	23	has	have	VERB
ejpam-3942	11	24	a	a	DET
ejpam-3942	11	25	special	special	ADJ
ejpam-3942	11	26	and	and	CCONJ
ejpam-3942	11	27	very	very	ADV
ejpam-3942	11	28	important	important	ADJ
ejpam-3942	11	29	role	role	NOUN
ejpam-3942	11	30	in	in	ADP
ejpam-3942	11	31	geometrical	geometrical	ADJ
ejpam-3942	11	32	methods	method	NOUN
ejpam-3942	11	33	allowing	allow	VERB
ejpam-3942	11	34	to	to	PART
ejpam-3942	11	35	solve	solve	VERB
ejpam-3942	11	36	a	a	DET
ejpam-3942	11	37	broad	broad	ADJ
ejpam-3942	11	38	scope	scope	NOUN
ejpam-3942	11	39	of	of	ADP
ejpam-3942	11	40	problems	problem	NOUN
ejpam-3942	11	41	.	.	PUNCT
ejpam-3942	12	1	rarely	rarely	ADV
ejpam-3942	12	2	mentioned	mention	VERB
ejpam-3942	12	3	in	in	ADP
ejpam-3942	12	4	scientific	scientific	ADJ
ejpam-3942	12	5	-	-	PUNCT
ejpam-3942	12	6	methodical	methodical	ADJ
ejpam-3942	12	7	literature	literature	NOUN
ejpam-3942	12	8	,	,	PUNCT
ejpam-3942	12	9	the	the	DET
ejpam-3942	12	10	area	area	NOUN
ejpam-3942	12	11	method	method	NOUN
ejpam-3942	12	12	is	be	AUX
ejpam-3942	12	13	nonetheless	nonetheless	ADV
ejpam-3942	12	14	often	often	ADV
ejpam-3942	12	15	used	use	VERB
ejpam-3942	12	16	to	to	PART
ejpam-3942	12	17	solve	solve	VERB
ejpam-3942	12	18	problems	problem	NOUN
ejpam-3942	12	19	in	in	ADP
ejpam-3942	12	20	mathematical	mathematical	ADJ
ejpam-3942	12	21	olympiads	olympiad	NOUN
ejpam-3942	12	22	and	and	CCONJ
ejpam-3942	12	23	other	other	ADJ
ejpam-3942	12	24	competition	competition	NOUN
ejpam-3942	12	25	events	event	NOUN
ejpam-3942	12	26	.	.	PUNCT
ejpam-3942	13	1	the	the	DET
ejpam-3942	13	2	works	work	NOUN
ejpam-3942	13	3	[	[	X
ejpam-3942	13	4	2	2	NUM
ejpam-3942	13	5	-	-	SYM
ejpam-3942	13	6	7	7	NUM
ejpam-3942	13	7	]	]	PUNCT
ejpam-3942	13	8	describe	describe	VERB
ejpam-3942	13	9	the	the	DET
ejpam-3942	13	10	ways	way	NOUN
ejpam-3942	13	11	to	to	PART
ejpam-3942	13	12	solve	solve	VERB
ejpam-3942	13	13	some	some	DET
ejpam-3942	13	14	problems	problem	NOUN
ejpam-3942	13	15	by	by	ADP
ejpam-3942	13	16	the	the	DET
ejpam-3942	13	17	area	area	NOUN
ejpam-3942	13	18	method	method	NOUN
ejpam-3942	13	19	.	.	PUNCT
ejpam-3942	14	1	also	also	ADV
ejpam-3942	14	2	lets	let	VERB
ejpam-3942	14	3	mention	mention	VERB
ejpam-3942	14	4	[	[	X
ejpam-3942	14	5	1	1	NUM
ejpam-3942	14	6	]	]	PUNCT
ejpam-3942	14	7	,	,	PUNCT
ejpam-3942	14	8	co	co	VERB
ejpam-3942	14	9	-	-	VERB
ejpam-3942	14	10	authored	author	VERB
ejpam-3942	14	11	by	by	ADP
ejpam-3942	14	12	the	the	DET
ejpam-3942	14	13	first	first	ADJ
ejpam-3942	14	14	author	author	NOUN
ejpam-3942	14	15	,	,	PUNCT
ejpam-3942	14	16	where	where	SCONJ
ejpam-3942	14	17	,	,	PUNCT
ejpam-3942	14	18	using	use	VERB
ejpam-3942	14	19	the	the	DET
ejpam-3942	14	20	area	area	NOUN
ejpam-3942	14	21	as	as	ADP
ejpam-3942	14	22	an	an	DET
ejpam-3942	14	23	auxiliary	auxiliary	ADJ
ejpam-3942	14	24	element	element	NOUN
ejpam-3942	14	25	,	,	PUNCT
ejpam-3942	14	26	the	the	DET
ejpam-3942	14	27	solution	solution	NOUN
ejpam-3942	14	28	is	be	AUX
ejpam-3942	14	29	found	find	VERB
ejpam-3942	14	30	in	in	ADP
ejpam-3942	14	31	a	a	DET
ejpam-3942	14	32	quite	quite	ADV
ejpam-3942	14	33	simple	simple	ADJ
ejpam-3942	14	34	and	and	CCONJ
ejpam-3942	14	35	smart	smart	ADJ
ejpam-3942	14	36	way	way	NOUN
ejpam-3942	14	37	.	.	PUNCT
ejpam-3942	15	1	the	the	DET
ejpam-3942	15	2	area	area	NOUN
ejpam-3942	15	3	method	method	NOUN
ejpam-3942	15	4	involves	involve	VERB
ejpam-3942	15	5	various	various	ADJ
ejpam-3942	15	6	properties	property	NOUN
ejpam-3942	15	7	of	of	ADP
ejpam-3942	15	8	areas	area	NOUN
ejpam-3942	15	9	to	to	PART
ejpam-3942	15	10	establish	establish	VERB
ejpam-3942	15	11	the	the	DET
ejpam-3942	15	12	relations	relation	NOUN
ejpam-3942	15	13	between	between	ADP
ejpam-3942	15	14	the	the	DET
ejpam-3942	15	15	problem	problem	NOUN
ejpam-3942	15	16	data	datum	NOUN
ejpam-3942	15	17	and	and	CCONJ
ejpam-3942	15	18	the	the	DET
ejpam-3942	15	19	unknowns	unknown	NOUN
ejpam-3942	15	20	.	.	PUNCT
ejpam-3942	16	1	the	the	DET
ejpam-3942	16	2	most	most	ADV
ejpam-3942	16	3	often	often	ADV
ejpam-3942	16	4	used	use	VERB
ejpam-3942	16	5	ones	one	NOUN
ejpam-3942	16	6	are	be	AUX
ejpam-3942	16	7	the	the	DET
ejpam-3942	16	8	additive	additive	ADJ
ejpam-3942	16	9	property	property	NOUN
ejpam-3942	16	10	and	and	CCONJ
ejpam-3942	16	11	the	the	DET
ejpam-3942	16	12	property	property	NOUN
ejpam-3942	16	13	of	of	ADP
ejpam-3942	16	14	the	the	DET
ejpam-3942	16	15	ratio	ratio	NOUN
ejpam-3942	16	16	of	of	ADP
ejpam-3942	16	17	areas	area	NOUN
ejpam-3942	16	18	which	which	PRON
ejpam-3942	16	19	help	help	VERB
ejpam-3942	16	20	to	to	PART
ejpam-3942	16	21	reduce	reduce	VERB
ejpam-3942	16	22	the	the	DET
ejpam-3942	16	23	problem	problem	NOUN
ejpam-3942	16	24	to	to	ADP
ejpam-3942	16	25	the	the	DET
ejpam-3942	16	26	solution	solution	NOUN
ejpam-3942	16	27	of	of	ADP
ejpam-3942	16	28	some	some	DET
ejpam-3942	16	29	equation	equation	NOUN
ejpam-3942	16	30	or	or	CCONJ
ejpam-3942	16	31	to	to	ADP
ejpam-3942	16	32	direct	direct	ADJ
ejpam-3942	16	33	calculation	calculation	NOUN
ejpam-3942	16	34	.	.	PUNCT
ejpam-3942	17	1	note	note	VERB
ejpam-3942	17	2	that	that	SCONJ
ejpam-3942	17	3	the	the	DET
ejpam-3942	17	4	area	area	NOUN
ejpam-3942	17	5	method	method	NOUN
ejpam-3942	17	6	is	be	AUX
ejpam-3942	17	7	used	use	VERB
ejpam-3942	17	8	to	to	PART
ejpam-3942	17	9	solve	solve	VERB
ejpam-3942	17	10	the	the	DET
ejpam-3942	17	11	problems	problem	NOUN
ejpam-3942	17	12	which	which	PRON
ejpam-3942	17	13	involve	involve	VERB
ejpam-3942	17	14	areas	area	NOUN
ejpam-3942	17	15	,	,	PUNCT
ejpam-3942	17	16	and	and	CCONJ
ejpam-3942	17	17	it	it	PRON
ejpam-3942	17	18	is	be	AUX
ejpam-3942	17	19	especially	especially	ADV
ejpam-3942	17	20	important	important	ADJ
ejpam-3942	17	21	for	for	ADP
ejpam-3942	17	22	those	those	DET
ejpam-3942	17	23	problems	problem	NOUN
ejpam-3942	17	24	which	which	PRON
ejpam-3942	17	25	do	do	AUX
ejpam-3942	17	26	not	not	PART
ejpam-3942	17	27	involve	involve	VERB
ejpam-3942	17	28	areas	area	NOUN
ejpam-3942	17	29	.	.	PUNCT
ejpam-3942	18	1	in	in	ADP
ejpam-3942	18	2	the	the	DET
ejpam-3942	18	3	latter	latter	ADJ
ejpam-3942	18	4	ones	one	NOUN
ejpam-3942	18	5	,	,	PUNCT
ejpam-3942	18	6	the	the	DET
ejpam-3942	18	7	area	area	NOUN
ejpam-3942	18	8	is	be	AUX
ejpam-3942	18	9	introduced	introduce	VERB
ejpam-3942	18	10	to	to	ADP
ejpam-3942	18	11	the	the	DET
ejpam-3942	18	12	problem	problem	NOUN
ejpam-3942	18	13	as	as	ADP
ejpam-3942	18	14	an	an	DET
ejpam-3942	18	15	auxiliary	auxiliary	ADJ
ejpam-3942	18	16	element	element	NOUN
ejpam-3942	18	17	.	.	PUNCT
ejpam-3942	19	1	despite	despite	SCONJ
ejpam-3942	19	2	looking	look	VERB
ejpam-3942	19	3	obvious	obvious	ADJ
ejpam-3942	19	4	,	,	PUNCT
ejpam-3942	19	5	the	the	DET
ejpam-3942	19	6	area	area	NOUN
ejpam-3942	19	7	method	method	NOUN
ejpam-3942	19	8	is	be	AUX
ejpam-3942	19	9	unfamiliar	unfamiliar	ADJ
ejpam-3942	19	10	to	to	ADP
ejpam-3942	19	11	majority	majority	NOUN
ejpam-3942	19	12	of	of	ADP
ejpam-3942	19	13	teachers	teacher	NOUN
ejpam-3942	19	14	and	and	CCONJ
ejpam-3942	19	15	students	student	NOUN
ejpam-3942	19	16	due	due	ADP
ejpam-3942	19	17	to	to	ADP
ejpam-3942	19	18	the	the	DET
ejpam-3942	19	19	current	current	ADJ
ejpam-3942	19	20	∗corresponding	∗corresponding	NOUN
ejpam-3942	19	21	author	author	NOUN
ejpam-3942	19	22	.	.	PUNCT
ejpam-3942	20	1	doi	doi	NOUN
ejpam-3942	20	2	:	:	PUNCT
ejpam-3942	20	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3942	https://doi.org/10.29020/nybg.ejpam.v14i2.3942	VERB
ejpam-3942	20	4	email	email	NOUN
ejpam-3942	20	5	addresses	address	NOUN
ejpam-3942	20	6	:	:	PUNCT
ejpam-3942	20	7	samed59@bk.ru	samed59@bk.ru	PROPN
ejpam-3942	20	8	(	(	PUNCT
ejpam-3942	20	9	s.	s.	PROPN
ejpam-3942	20	10	j.aliyev	j.aliyev	PROPN
ejpam-3942	20	11	)	)	PUNCT
ejpam-3942	20	12	,	,	PUNCT
ejpam-3942	20	13	shahinaghazade@bsu.edu.az	shahinaghazade@bsu.edu.az	PROPN
ejpam-3942	20	14	(	(	PUNCT
ejpam-3942	20	15	s.	s.	PROPN
ejpam-3942	20	16	m.aghazade),a.q.z.41@mail.ru	m.aghazade),a.q.z.41@mail.ru	NUM
ejpam-3942	20	17	(	(	PUNCT
ejpam-3942	20	18	g.	g.	PROPN
ejpam-3942	20	19	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3942	20	20	)	)	PUNCT
ejpam-3942	20	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3942	21	1	601	601	NUM
ejpam-3942	21	2	c	c	AUX
ejpam-3942	21	3	©	©	PROPN
ejpam-3942	21	4	2021	2021	NUM
ejpam-3942	21	5	ejpam	ejpam	VERB
ejpam-3942	21	6	all	all	DET
ejpam-3942	21	7	rights	right	NOUN
ejpam-3942	21	8	reserved	reserve	VERB
ejpam-3942	21	9	.	.	PUNCT
ejpam-3942	22	1	s.	s.	PROPN
ejpam-3942	22	2	j.aliyev	j.aliyev	PROPN
ejpam-3942	22	3	,	,	PUNCT
ejpam-3942	22	4	s.	s.	PROPN
ejpam-3942	22	5	m.aghazade	m.aghazade	PROPN
ejpam-3942	22	6	,	,	PUNCT
ejpam-3942	22	7	g.	g.	PROPN
ejpam-3942	22	8	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3942	22	9	/	/	SYM
ejpam-3942	22	10	eur	eur	PROPN
ejpam-3942	22	11	.	.	PUNCT
ejpam-3942	23	1	j.	j.	PROPN
ejpam-3942	23	2	pure	pure	PROPN
ejpam-3942	23	3	appl	appl	PROPN
ejpam-3942	23	4	.	.	PROPN
ejpam-3942	23	5	math	math	PROPN
ejpam-3942	23	6	,	,	PUNCT
ejpam-3942	23	7	14	14	NUM
ejpam-3942	23	8	(	(	PUNCT
ejpam-3942	23	9	2	2	NUM
ejpam-3942	23	10	)	)	PUNCT
ejpam-3942	23	11	(	(	PUNCT
ejpam-3942	23	12	2021	2021	NUM
ejpam-3942	23	13	)	)	PUNCT
ejpam-3942	23	14	,	,	PUNCT
ejpam-3942	23	15	601	601	NUM
ejpam-3942	23	16	-	-	SYM
ejpam-3942	23	17	607	607	NUM
ejpam-3942	23	18	602	602	NUM
ejpam-3942	23	19	figure	figure	NOUN
ejpam-3942	23	20	1	1	NUM
ejpam-3942	23	21	:	:	PUNCT
ejpam-3942	23	22	triangle	triangle	VERB
ejpam-3942	23	23	abc	abc	PROPN
ejpam-3942	23	24	with	with	ADP
ejpam-3942	23	25	bisector	bisector	NOUN
ejpam-3942	23	26	ad	ad	NOUN
ejpam-3942	23	27	.	.	PUNCT
ejpam-3942	24	1	situation	situation	NOUN
ejpam-3942	24	2	with	with	ADP
ejpam-3942	24	3	teaching	teaching	NOUN
ejpam-3942	24	4	geometry	geometry	NOUN
ejpam-3942	24	5	and	and	CCONJ
ejpam-3942	24	6	the	the	DET
ejpam-3942	24	7	methods	method	NOUN
ejpam-3942	24	8	of	of	ADP
ejpam-3942	24	9	solving	solve	VERB
ejpam-3942	24	10	geometrical	geometrical	ADJ
ejpam-3942	24	11	problems	problem	NOUN
ejpam-3942	24	12	in	in	ADP
ejpam-3942	24	13	secondary	secondary	ADJ
ejpam-3942	24	14	schools	school	NOUN
ejpam-3942	24	15	.	.	PUNCT
ejpam-3942	25	1	how	how	SCONJ
ejpam-3942	25	2	do	do	AUX
ejpam-3942	25	3	we	we	PRON
ejpam-3942	25	4	use	use	VERB
ejpam-3942	25	5	the	the	DET
ejpam-3942	25	6	area	area	NOUN
ejpam-3942	25	7	method	method	NOUN
ejpam-3942	25	8	?	?	PUNCT
ejpam-3942	26	1	we	we	PRON
ejpam-3942	26	2	consider	consider	VERB
ejpam-3942	26	3	the	the	DET
ejpam-3942	26	4	area	area	NOUN
ejpam-3942	26	5	of	of	ADP
ejpam-3942	26	6	the	the	DET
ejpam-3942	26	7	given	give	VERB
ejpam-3942	26	8	figure	figure	NOUN
ejpam-3942	26	9	as	as	ADP
ejpam-3942	26	10	a	a	DET
ejpam-3942	26	11	sum	sum	NOUN
ejpam-3942	26	12	of	of	ADP
ejpam-3942	26	13	the	the	DET
ejpam-3942	26	14	areas	area	NOUN
ejpam-3942	26	15	of	of	ADP
ejpam-3942	26	16	its	its	PRON
ejpam-3942	26	17	parts	part	NOUN
ejpam-3942	26	18	.	.	PUNCT
ejpam-3942	27	1	we	we	PRON
ejpam-3942	27	2	calculate	calculate	VERB
ejpam-3942	27	3	the	the	DET
ejpam-3942	27	4	areas	area	NOUN
ejpam-3942	27	5	of	of	ADP
ejpam-3942	27	6	each	each	DET
ejpam-3942	27	7	part	part	NOUN
ejpam-3942	27	8	in	in	ADP
ejpam-3942	27	9	a	a	DET
ejpam-3942	27	10	suitable	suitable	ADJ
ejpam-3942	27	11	way	way	NOUN
ejpam-3942	27	12	to	to	PART
ejpam-3942	27	13	obtain	obtain	VERB
ejpam-3942	27	14	the	the	DET
ejpam-3942	27	15	equation	equation	NOUN
ejpam-3942	27	16	which	which	PRON
ejpam-3942	27	17	either	either	CCONJ
ejpam-3942	27	18	gives	give	VERB
ejpam-3942	27	19	the	the	DET
ejpam-3942	27	20	solution	solution	NOUN
ejpam-3942	27	21	or	or	CCONJ
ejpam-3942	27	22	significantly	significantly	ADV
ejpam-3942	27	23	facilitates	facilitate	VERB
ejpam-3942	27	24	its	its	PRON
ejpam-3942	27	25	search	search	NOUN
ejpam-3942	27	26	.	.	PUNCT
ejpam-3942	28	1	to	to	PART
ejpam-3942	28	2	illustrate	illustrate	VERB
ejpam-3942	28	3	the	the	DET
ejpam-3942	28	4	method	method	NOUN
ejpam-3942	28	5	,	,	PUNCT
ejpam-3942	28	6	we	we	PRON
ejpam-3942	28	7	will	will	AUX
ejpam-3942	28	8	consider	consider	VERB
ejpam-3942	28	9	simplest	simple	ADJ
ejpam-3942	28	10	problems	problem	NOUN
ejpam-3942	28	11	where	where	SCONJ
ejpam-3942	28	12	the	the	DET
ejpam-3942	28	13	area	area	NOUN
ejpam-3942	28	14	can	can	AUX
ejpam-3942	28	15	be	be	AUX
ejpam-3942	28	16	calculated	calculate	VERB
ejpam-3942	28	17	in	in	ADP
ejpam-3942	28	18	two	two	NUM
ejpam-3942	28	19	ways	way	NOUN
ejpam-3942	28	20	.	.	PUNCT
ejpam-3942	29	1	for	for	ADP
ejpam-3942	29	2	example	example	NOUN
ejpam-3942	29	3	,	,	PUNCT
ejpam-3942	29	4	let	let	VERB
ejpam-3942	29	5	an	an	DET
ejpam-3942	29	6	isosceles	isoscele	NOUN
ejpam-3942	29	7	triangle	triangle	NOUN
ejpam-3942	29	8	be	be	AUX
ejpam-3942	29	9	given	give	VERB
ejpam-3942	29	10	,	,	PUNCT
ejpam-3942	29	11	and	and	CCONJ
ejpam-3942	29	12	let	let	VERB
ejpam-3942	29	13	its	its	PRON
ejpam-3942	29	14	base	base	NOUN
ejpam-3942	29	15	and	and	CCONJ
ejpam-3942	29	16	the	the	DET
ejpam-3942	29	17	height	height	NOUN
ejpam-3942	29	18	drawn	draw	VERB
ejpam-3942	29	19	to	to	ADP
ejpam-3942	29	20	its	its	PRON
ejpam-3942	29	21	base	base	NOUN
ejpam-3942	29	22	be	be	AUX
ejpam-3942	29	23	known	know	VERB
ejpam-3942	29	24	;	;	PUNCT
ejpam-3942	29	25	find	find	VERB
ejpam-3942	29	26	the	the	DET
ejpam-3942	29	27	height	height	NOUN
ejpam-3942	29	28	drawn	draw	VERB
ejpam-3942	29	29	to	to	ADP
ejpam-3942	29	30	its	its	PRON
ejpam-3942	29	31	side	side	NOUN
ejpam-3942	29	32	.	.	PUNCT
ejpam-3942	30	1	first	first	ADV
ejpam-3942	30	2	,	,	PUNCT
ejpam-3942	30	3	the	the	DET
ejpam-3942	30	4	area	area	NOUN
ejpam-3942	30	5	of	of	ADP
ejpam-3942	30	6	this	this	DET
ejpam-3942	30	7	triangle	triangle	NOUN
ejpam-3942	30	8	is	be	AUX
ejpam-3942	30	9	half	half	NOUN
ejpam-3942	30	10	of	of	ADP
ejpam-3942	30	11	the	the	DET
ejpam-3942	30	12	product	product	NOUN
ejpam-3942	30	13	of	of	ADP
ejpam-3942	30	14	its	its	PRON
ejpam-3942	30	15	base	base	NOUN
ejpam-3942	30	16	and	and	CCONJ
ejpam-3942	30	17	the	the	DET
ejpam-3942	30	18	height	height	NOUN
ejpam-3942	30	19	drawn	draw	VERB
ejpam-3942	30	20	to	to	ADP
ejpam-3942	30	21	the	the	DET
ejpam-3942	30	22	base	base	NOUN
ejpam-3942	30	23	.	.	PUNCT
ejpam-3942	31	1	on	on	ADP
ejpam-3942	31	2	the	the	DET
ejpam-3942	31	3	other	other	ADJ
ejpam-3942	31	4	hand	hand	NOUN
ejpam-3942	31	5	,	,	PUNCT
ejpam-3942	31	6	it	it	PRON
ejpam-3942	31	7	equals	equal	VERB
ejpam-3942	31	8	to	to	ADP
ejpam-3942	31	9	the	the	DET
ejpam-3942	31	10	half	half	NOUN
ejpam-3942	31	11	of	of	ADP
ejpam-3942	31	12	the	the	DET
ejpam-3942	31	13	product	product	NOUN
ejpam-3942	31	14	of	of	ADP
ejpam-3942	31	15	the	the	DET
ejpam-3942	31	16	side	side	NOUN
ejpam-3942	31	17	and	and	CCONJ
ejpam-3942	31	18	the	the	DET
ejpam-3942	31	19	corresponding	corresponding	ADJ
ejpam-3942	31	20	height	height	NOUN
ejpam-3942	31	21	,	,	PUNCT
ejpam-3942	31	22	with	with	ADP
ejpam-3942	31	23	the	the	DET
ejpam-3942	31	24	side	side	NOUN
ejpam-3942	31	25	of	of	ADP
ejpam-3942	31	26	triangle	triangle	NOUN
ejpam-3942	31	27	easily	easily	ADV
ejpam-3942	31	28	calculated	calculate	VERB
ejpam-3942	31	29	by	by	ADP
ejpam-3942	31	30	the	the	DET
ejpam-3942	31	31	pythagorean	pythagorean	PROPN
ejpam-3942	31	32	theorem	theorem	PROPN
ejpam-3942	31	33	.	.	PUNCT
ejpam-3942	32	1	lets	lets	AUX
ejpam-3942	32	2	give	give	VERB
ejpam-3942	32	3	some	some	DET
ejpam-3942	32	4	examples	example	NOUN
ejpam-3942	32	5	which	which	PRON
ejpam-3942	32	6	illustrate	illustrate	VERB
ejpam-3942	32	7	the	the	DET
ejpam-3942	32	8	use	use	NOUN
ejpam-3942	32	9	of	of	ADP
ejpam-3942	32	10	area	area	NOUN
ejpam-3942	32	11	method	method	NOUN
ejpam-3942	32	12	.	.	PUNCT
ejpam-3942	33	1	find	find	VERB
ejpam-3942	33	2	the	the	DET
ejpam-3942	33	3	bisector	bisector	NOUN
ejpam-3942	33	4	ad	ad	NOUN
ejpam-3942	33	5	of	of	ADP
ejpam-3942	33	6	the	the	DET
ejpam-3942	33	7	triangle	triangle	NOUN
ejpam-3942	33	8	abc	abc	PROPN
ejpam-3942	33	9	,	,	PUNCT
ejpam-3942	33	10	where	where	SCONJ
ejpam-3942	33	11	ab	ab	PROPN
ejpam-3942	33	12	=	=	PUNCT
ejpam-3942	33	13	c	c	PROPN
ejpam-3942	33	14	,	,	PUNCT
ejpam-3942	33	15	ac	ac	PROPN
ejpam-3942	33	16	=	=	SYM
ejpam-3942	33	17	b	b	PROPN
ejpam-3942	33	18	,	,	PUNCT
ejpam-3942	33	19	∠bac	∠bac	PROPN
ejpam-3942	33	20	=	=	SYM
ejpam-3942	34	1	α	α	X
ejpam-3942	34	2	.	.	PUNCT
ejpam-3942	34	3	lets	lets	AUX
ejpam-3942	34	4	calculate	calculate	VERB
ejpam-3942	34	5	the	the	DET
ejpam-3942	34	6	area	area	NOUN
ejpam-3942	34	7	of	of	ADP
ejpam-3942	34	8	the	the	DET
ejpam-3942	34	9	triangle	triangle	NOUN
ejpam-3942	34	10	abc	abc	PROPN
ejpam-3942	34	11	(	(	PUNCT
ejpam-3942	34	12	fig	fig	NOUN
ejpam-3942	34	13	.	.	PUNCT
ejpam-3942	35	1	1	1	NUM
ejpam-3942	35	2	):	):	PUNCT
ejpam-3942	35	3	sabc	sabc	PROPN
ejpam-3942	35	4	=	=	SYM
ejpam-3942	35	5	sabd	sabd	PROPN
ejpam-3942	35	6	+	+	NUM
ejpam-3942	35	7	sadc	sadc	PROPN
ejpam-3942	35	8	,	,	PUNCT
ejpam-3942	35	9	(	(	PUNCT
ejpam-3942	35	10	1	1	X
ejpam-3942	35	11	)	)	PUNCT
ejpam-3942	35	12	where	where	SCONJ
ejpam-3942	35	13	sabc	sabc	PROPN
ejpam-3942	35	14	=	=	PROPN
ejpam-3942	35	15	1	1	NUM
ejpam-3942	35	16	2	2	NUM
ejpam-3942	35	17	·	·	SYM
ejpam-3942	35	18	ab	ab	X
ejpam-3942	35	19	·	·	PUNCT
ejpam-3942	35	20	ac	ac	PROPN
ejpam-3942	35	21	·	·	PUNCT
ejpam-3942	35	22	sinα	sinα	PROPN
ejpam-3942	35	23	=	=	SYM
ejpam-3942	35	24	1	1	NUM
ejpam-3942	35	25	2	2	NUM
ejpam-3942	35	26	·	·	PUNCT
ejpam-3942	35	27	c	c	X
ejpam-3942	35	28	·	·	PUNCT
ejpam-3942	35	29	b	b	X
ejpam-3942	35	30	·	·	PUNCT
ejpam-3942	35	31	sinα	sinα	NOUN
ejpam-3942	35	32	,	,	PUNCT
ejpam-3942	35	33	sabd	sabd	NOUN
ejpam-3942	35	34	=	=	SYM
ejpam-3942	35	35	1	1	NUM
ejpam-3942	35	36	2	2	NUM
ejpam-3942	35	37	·	·	SYM
ejpam-3942	35	38	ab	ab	X
ejpam-3942	35	39	·	·	SYM
ejpam-3942	35	40	ad	ad	X
ejpam-3942	35	41	·	·	PUNCT
ejpam-3942	35	42	sin	sin	NOUN
ejpam-3942	35	43	α	α	NOUN
ejpam-3942	35	44	2	2	NUM
ejpam-3942	35	45	=	=	SYM
ejpam-3942	35	46	1	1	NUM
ejpam-3942	35	47	2	2	NUM
ejpam-3942	35	48	·	·	PUNCT
ejpam-3942	35	49	c	c	NOUN
ejpam-3942	35	50	·	·	SYM
ejpam-3942	35	51	ad	ad	X
ejpam-3942	35	52	·	·	PUNCT
ejpam-3942	35	53	sin	sin	NOUN
ejpam-3942	35	54	α	α	PROPN
ejpam-3942	35	55	2	2	NUM
ejpam-3942	35	56	,	,	PUNCT
ejpam-3942	35	57	sadc	sadc	NOUN
ejpam-3942	35	58	=	=	SYM
ejpam-3942	35	59	1	1	NUM
ejpam-3942	35	60	2	2	NUM
ejpam-3942	35	61	·	·	SYM
ejpam-3942	35	62	ad	ad	X
ejpam-3942	35	63	·	·	SYM
ejpam-3942	35	64	ac	ac	X
ejpam-3942	35	65	·	·	PUNCT
ejpam-3942	35	66	sin	sin	NOUN
ejpam-3942	35	67	α	α	NOUN
ejpam-3942	35	68	2	2	NUM
ejpam-3942	35	69	=	=	SYM
ejpam-3942	35	70	1	1	NUM
ejpam-3942	35	71	2	2	NUM
ejpam-3942	35	72	·	·	SYM
ejpam-3942	35	73	b	b	X
ejpam-3942	35	74	·	·	SYM
ejpam-3942	35	75	ad	ad	X
ejpam-3942	35	76	·	·	PUNCT
ejpam-3942	35	77	sin	sin	NOUN
ejpam-3942	35	78	α	α	NOUN
ejpam-3942	35	79	2	2	NUM
ejpam-3942	35	80	.	.	PUNCT
ejpam-3942	36	1	then	then	ADV
ejpam-3942	36	2	,	,	PUNCT
ejpam-3942	36	3	substituting	substitute	VERB
ejpam-3942	36	4	the	the	DET
ejpam-3942	36	5	obtained	obtain	VERB
ejpam-3942	36	6	expressions	expression	NOUN
ejpam-3942	36	7	into	into	ADP
ejpam-3942	36	8	(	(	PUNCT
ejpam-3942	36	9	1	1	NUM
ejpam-3942	36	10	)	)	PUNCT
ejpam-3942	36	11	,	,	PUNCT
ejpam-3942	36	12	we	we	PRON
ejpam-3942	36	13	get	get	VERB
ejpam-3942	36	14	the	the	DET
ejpam-3942	36	15	equation	equation	NOUN
ejpam-3942	36	16	1	1	NUM
ejpam-3942	36	17	2	2	NUM
ejpam-3942	36	18	·	·	PUNCT
ejpam-3942	36	19	c	c	X
ejpam-3942	36	20	·	·	PUNCT
ejpam-3942	36	21	b	b	X
ejpam-3942	36	22	·	·	PUNCT
ejpam-3942	36	23	sinα	sinα	NOUN
ejpam-3942	36	24	=	=	SYM
ejpam-3942	36	25	1	1	NUM
ejpam-3942	36	26	2	2	NUM
ejpam-3942	36	27	·	·	PUNCT
ejpam-3942	36	28	c	c	NOUN
ejpam-3942	36	29	·	·	SYM
ejpam-3942	36	30	ad	ad	X
ejpam-3942	36	31	·	·	PUNCT
ejpam-3942	36	32	sin	sin	NOUN
ejpam-3942	36	33	α	α	NOUN
ejpam-3942	36	34	2	2	NUM
ejpam-3942	37	1	+	+	CCONJ
ejpam-3942	37	2	1	1	NUM
ejpam-3942	37	3	2	2	NUM
ejpam-3942	37	4	·	·	SYM
ejpam-3942	37	5	b	b	X
ejpam-3942	37	6	·	·	SYM
ejpam-3942	37	7	ad	ad	X
ejpam-3942	37	8	·	·	PUNCT
ejpam-3942	37	9	sin	sin	NOUN
ejpam-3942	37	10	α	α	NOUN
ejpam-3942	37	11	2	2	NUM
ejpam-3942	37	12	.	.	PUNCT
ejpam-3942	38	1	after	after	ADP
ejpam-3942	38	2	some	some	DET
ejpam-3942	38	3	transformations	transformation	NOUN
ejpam-3942	38	4	we	we	PRON
ejpam-3942	38	5	obtain	obtain	VERB
ejpam-3942	38	6	ad	ad	NOUN
ejpam-3942	38	7	=	=	SYM
ejpam-3942	38	8	2	2	NUM
ejpam-3942	38	9	·	·	PUNCT
ejpam-3942	38	10	c	c	X
ejpam-3942	38	11	·	·	PUNCT
ejpam-3942	38	12	b	b	X
ejpam-3942	38	13	·	·	PUNCT
ejpam-3942	38	14	cos	cos	ADP
ejpam-3942	38	15	α2	α2	PROPN
ejpam-3942	38	16	b+	b+	PUNCT
ejpam-3942	38	17	c	c	X
ejpam-3942	38	18	.	.	PUNCT
ejpam-3942	39	1	the	the	DET
ejpam-3942	39	2	conditions	condition	NOUN
ejpam-3942	39	3	of	of	ADP
ejpam-3942	39	4	this	this	DET
ejpam-3942	39	5	problem	problem	NOUN
ejpam-3942	39	6	do	do	AUX
ejpam-3942	39	7	not	not	PART
ejpam-3942	39	8	involve	involve	VERB
ejpam-3942	39	9	areas	area	NOUN
ejpam-3942	39	10	,	,	PUNCT
ejpam-3942	39	11	but	but	CCONJ
ejpam-3942	39	12	note	note	VERB
ejpam-3942	39	13	that	that	SCONJ
ejpam-3942	39	14	the	the	DET
ejpam-3942	39	15	bisector	bisector	NOUN
ejpam-3942	39	16	divides	divide	VERB
ejpam-3942	39	17	the	the	DET
ejpam-3942	39	18	triangle	triangle	NOUN
ejpam-3942	39	19	into	into	ADP
ejpam-3942	39	20	the	the	DET
ejpam-3942	39	21	parts	part	NOUN
ejpam-3942	39	22	whose	whose	DET
ejpam-3942	39	23	areas	area	NOUN
ejpam-3942	39	24	can	can	AUX
ejpam-3942	39	25	be	be	AUX
ejpam-3942	39	26	easily	easily	ADV
ejpam-3942	39	27	calculated	calculate	VERB
ejpam-3942	39	28	using	use	VERB
ejpam-3942	39	29	the	the	DET
ejpam-3942	39	30	conditions	condition	NOUN
ejpam-3942	39	31	of	of	ADP
ejpam-3942	39	32	the	the	DET
ejpam-3942	39	33	s.	s.	PROPN
ejpam-3942	39	34	j.aliyev	j.aliyev	PROPN
ejpam-3942	39	35	,	,	PUNCT
ejpam-3942	39	36	s.	s.	PROPN
ejpam-3942	39	37	m.aghazade	m.aghazade	PROPN
ejpam-3942	39	38	,	,	PUNCT
ejpam-3942	39	39	g.	g.	PROPN
ejpam-3942	39	40	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3942	39	41	/	/	SYM
ejpam-3942	39	42	eur	eur	PROPN
ejpam-3942	39	43	.	.	PUNCT
ejpam-3942	40	1	j.	j.	PROPN
ejpam-3942	40	2	pure	pure	PROPN
ejpam-3942	40	3	appl	appl	PROPN
ejpam-3942	40	4	.	.	PROPN
ejpam-3942	40	5	math	math	PROPN
ejpam-3942	40	6	,	,	PUNCT
ejpam-3942	40	7	14	14	NUM
ejpam-3942	40	8	(	(	PUNCT
ejpam-3942	40	9	2	2	NUM
ejpam-3942	40	10	)	)	PUNCT
ejpam-3942	40	11	(	(	PUNCT
ejpam-3942	40	12	2021	2021	NUM
ejpam-3942	40	13	)	)	PUNCT
ejpam-3942	40	14	,	,	PUNCT
ejpam-3942	40	15	601	601	NUM
ejpam-3942	40	16	-	-	SYM
ejpam-3942	40	17	607	607	NUM
ejpam-3942	40	18	603	603	NUM
ejpam-3942	40	19	figure	figure	NOUN
ejpam-3942	40	20	2	2	NUM
ejpam-3942	40	21	:	:	PUNCT
ejpam-3942	40	22	points	point	NOUN
ejpam-3942	40	23	o1	o1	PROPN
ejpam-3942	40	24	,	,	PUNCT
ejpam-3942	40	25	o2	o2	PROPN
ejpam-3942	40	26	,	,	PUNCT
ejpam-3942	40	27	o3	o3	PROPN
ejpam-3942	40	28	are	be	AUX
ejpam-3942	40	29	the	the	DET
ejpam-3942	40	30	centers	center	NOUN
ejpam-3942	40	31	of	of	ADP
ejpam-3942	40	32	the	the	DET
ejpam-3942	40	33	excircles	excircle	NOUN
ejpam-3942	40	34	of	of	ADP
ejpam-3942	40	35	the	the	DET
ejpam-3942	40	36	triangle	triangle	NOUN
ejpam-3942	40	37	abc	abc	PROPN
ejpam-3942	40	38	.	.	PROPN
ejpam-3942	40	39	problem	problem	NOUN
ejpam-3942	40	40	.	.	PUNCT
ejpam-3942	41	1	the	the	DET
ejpam-3942	41	2	area	area	NOUN
ejpam-3942	41	3	of	of	ADP
ejpam-3942	41	4	the	the	DET
ejpam-3942	41	5	triangle	triangle	NOUN
ejpam-3942	41	6	itself	itself	PRON
ejpam-3942	41	7	can	can	AUX
ejpam-3942	41	8	also	also	ADV
ejpam-3942	41	9	be	be	AUX
ejpam-3942	41	10	easily	easily	ADV
ejpam-3942	41	11	calculated	calculate	VERB
ejpam-3942	41	12	.	.	PUNCT
ejpam-3942	42	1	therefore	therefore	ADV
ejpam-3942	42	2	the	the	DET
ejpam-3942	42	3	area	area	NOUN
ejpam-3942	42	4	method	method	NOUN
ejpam-3942	42	5	is	be	AUX
ejpam-3942	42	6	useful	useful	ADJ
ejpam-3942	42	7	here	here	ADV
ejpam-3942	42	8	.	.	PUNCT
ejpam-3942	43	1	having	having	AUX
ejpam-3942	43	2	introduced	introduce	VERB
ejpam-3942	43	3	the	the	DET
ejpam-3942	43	4	area	area	NOUN
ejpam-3942	43	5	as	as	ADP
ejpam-3942	43	6	an	an	DET
ejpam-3942	43	7	auxiliary	auxiliary	ADJ
ejpam-3942	43	8	element	element	NOUN
ejpam-3942	43	9	,	,	PUNCT
ejpam-3942	43	10	we	we	PRON
ejpam-3942	43	11	solved	solve	VERB
ejpam-3942	43	12	the	the	DET
ejpam-3942	43	13	problem	problem	NOUN
ejpam-3942	43	14	in	in	ADP
ejpam-3942	43	15	a	a	DET
ejpam-3942	43	16	simple	simple	ADJ
ejpam-3942	43	17	way	way	NOUN
ejpam-3942	43	18	.	.	PUNCT
ejpam-3942	44	1	consider	consider	VERB
ejpam-3942	44	2	another	another	DET
ejpam-3942	44	3	problem	problem	NOUN
ejpam-3942	44	4	,	,	PUNCT
ejpam-3942	44	5	where	where	SCONJ
ejpam-3942	44	6	the	the	DET
ejpam-3942	44	7	additive	additive	ADJ
ejpam-3942	44	8	property	property	NOUN
ejpam-3942	44	9	of	of	ADP
ejpam-3942	44	10	area	area	NOUN
ejpam-3942	44	11	and	and	CCONJ
ejpam-3942	44	12	the	the	DET
ejpam-3942	44	13	formulas	formula	NOUN
ejpam-3942	44	14	for	for	ADP
ejpam-3942	44	15	the	the	DET
ejpam-3942	44	16	calculation	calculation	NOUN
ejpam-3942	44	17	of	of	ADP
ejpam-3942	44	18	areas	area	NOUN
ejpam-3942	44	19	help	help	VERB
ejpam-3942	44	20	to	to	PART
ejpam-3942	44	21	find	find	VERB
ejpam-3942	44	22	the	the	DET
ejpam-3942	44	23	lengths	length	NOUN
ejpam-3942	44	24	of	of	ADP
ejpam-3942	44	25	intervals	interval	NOUN
ejpam-3942	44	26	.	.	PUNCT
ejpam-3942	45	1	find	find	VERB
ejpam-3942	45	2	the	the	DET
ejpam-3942	45	3	radii	radius	NOUN
ejpam-3942	45	4	of	of	ADP
ejpam-3942	45	5	the	the	DET
ejpam-3942	45	6	incircle	incircle	NOUN
ejpam-3942	45	7	and	and	CCONJ
ejpam-3942	45	8	excircles	excircle	NOUN
ejpam-3942	45	9	of	of	ADP
ejpam-3942	45	10	the	the	DET
ejpam-3942	45	11	triangle	triangle	NOUN
ejpam-3942	45	12	abc	abc	PROPN
ejpam-3942	45	13	,	,	PUNCT
ejpam-3942	45	14	where	where	SCONJ
ejpam-3942	45	15	ab	ab	PROPN
ejpam-3942	45	16	=	=	SYM
ejpam-3942	45	17	15	15	NUM
ejpam-3942	45	18	,	,	PUNCT
ejpam-3942	45	19	bc	bc	PROPN
ejpam-3942	45	20	=	=	SYM
ejpam-3942	45	21	14	14	NUM
ejpam-3942	45	22	,	,	PUNCT
ejpam-3942	45	23	ac	ac	PROPN
ejpam-3942	45	24	=	=	PROPN
ejpam-3942	45	25	13	13	NUM
ejpam-3942	45	26	.	.	PUNCT
ejpam-3942	46	1	as	as	ADP
ejpam-3942	46	2	the	the	DET
ejpam-3942	46	3	semiperimeter	semiperimet	ADJ
ejpam-3942	46	4	p	p	NOUN
ejpam-3942	46	5	of	of	ADP
ejpam-3942	46	6	the	the	DET
ejpam-3942	46	7	triangle	triangle	NOUN
ejpam-3942	46	8	abc	abc	PROPN
ejpam-3942	46	9	is	be	AUX
ejpam-3942	46	10	equal	equal	ADJ
ejpam-3942	46	11	to	to	ADP
ejpam-3942	46	12	21	21	NUM
ejpam-3942	46	13	,	,	PUNCT
ejpam-3942	46	14	the	the	DET
ejpam-3942	46	15	area	area	NOUN
ejpam-3942	46	16	of	of	ADP
ejpam-3942	46	17	this	this	DET
ejpam-3942	46	18	triangle	triangle	NOUN
ejpam-3942	46	19	can	can	AUX
ejpam-3942	46	20	be	be	AUX
ejpam-3942	46	21	found	find	VERB
ejpam-3942	46	22	by	by	ADP
ejpam-3942	46	23	herons	heron	NOUN
ejpam-3942	46	24	formula	formula	NOUN
ejpam-3942	46	25	:	:	PUNCT
ejpam-3942	46	26	sabc	sabc	PROPN
ejpam-3942	46	27	=	=	PROPN
ejpam-3942	46	28	√	√	PROPN
ejpam-3942	46	29	p	p	NOUN
ejpam-3942	46	30	(	(	PUNCT
ejpam-3942	46	31	p−	p−	NOUN
ejpam-3942	46	32	a	a	NOUN
ejpam-3942	46	33	)	)	PUNCT
ejpam-3942	46	34	(	(	PUNCT
ejpam-3942	46	35	p−	p−	NOUN
ejpam-3942	46	36	b	b	NOUN
ejpam-3942	46	37	)	)	PUNCT
ejpam-3942	46	38	(	(	PUNCT
ejpam-3942	46	39	p−	p−	NOUN
ejpam-3942	46	40	c	c	NOUN
ejpam-3942	46	41	)	)	PUNCT
ejpam-3942	46	42	=	=	SYM
ejpam-3942	47	1	√	√	ADP
ejpam-3942	47	2	21	21	NUM
ejpam-3942	47	3	·	·	SYM
ejpam-3942	47	4	8	8	NUM
ejpam-3942	47	5	·	·	SYM
ejpam-3942	47	6	7	7	NUM
ejpam-3942	47	7	·	·	SYM
ejpam-3942	47	8	6	6	NUM
ejpam-3942	47	9	=	=	SYM
ejpam-3942	47	10	84	84	NUM
ejpam-3942	47	11	.	.	PUNCT
ejpam-3942	48	1	consequently	consequently	ADV
ejpam-3942	48	2	,	,	PUNCT
ejpam-3942	48	3	the	the	DET
ejpam-3942	48	4	radius	radius	NOUN
ejpam-3942	48	5	of	of	ADP
ejpam-3942	48	6	the	the	DET
ejpam-3942	48	7	incircle	incircle	NOUN
ejpam-3942	48	8	of	of	ADP
ejpam-3942	48	9	abc	abc	PROPN
ejpam-3942	48	10	is	be	AUX
ejpam-3942	48	11	equal	equal	ADJ
ejpam-3942	48	12	to	to	ADP
ejpam-3942	48	13	r	r	NOUN
ejpam-3942	48	14	=	=	SYM
ejpam-3942	48	15	sabc	sabc	PROPN
ejpam-3942	48	16	p	p	NOUN
ejpam-3942	48	17	=	=	PROPN
ejpam-3942	48	18	84	84	NUM
ejpam-3942	48	19	21	21	NUM
ejpam-3942	48	20	=	=	SYM
ejpam-3942	48	21	4	4	X
ejpam-3942	48	22	.	.	PUNCT
ejpam-3942	49	1	let	let	VERB
ejpam-3942	49	2	r1	r1	PROPN
ejpam-3942	49	3	,	,	PUNCT
ejpam-3942	49	4	r2	r2	PROPN
ejpam-3942	49	5	,	,	PUNCT
ejpam-3942	49	6	r3	r3	PROPN
ejpam-3942	49	7	be	be	VERB
ejpam-3942	49	8	the	the	DET
ejpam-3942	49	9	radii	radius	NOUN
ejpam-3942	49	10	of	of	ADP
ejpam-3942	49	11	the	the	DET
ejpam-3942	49	12	excircles	excircle	NOUN
ejpam-3942	49	13	of	of	ADP
ejpam-3942	49	14	the	the	DET
ejpam-3942	49	15	triangle	triangle	NOUN
ejpam-3942	49	16	abc	abc	PROPN
ejpam-3942	49	17	(	(	PUNCT
ejpam-3942	49	18	fig	fig	NOUN
ejpam-3942	49	19	.	.	PUNCT
ejpam-3942	50	1	2	2	NUM
ejpam-3942	50	2	)	)	PUNCT
ejpam-3942	50	3	.	.	PUNCT
ejpam-3942	51	1	lets	lets	AUX
ejpam-3942	51	2	first	first	ADV
ejpam-3942	51	3	find	find	VERB
ejpam-3942	51	4	r1	r1	PROPN
ejpam-3942	51	5	.	.	PUNCT
ejpam-3942	52	1	note	note	VERB
ejpam-3942	52	2	that	that	SCONJ
ejpam-3942	52	3	this	this	DET
ejpam-3942	52	4	radius	radius	NOUN
ejpam-3942	52	5	is	be	AUX
ejpam-3942	52	6	a	a	DET
ejpam-3942	52	7	height	height	NOUN
ejpam-3942	52	8	in	in	ADP
ejpam-3942	52	9	the	the	DET
ejpam-3942	52	10	triangles	triangle	NOUN
ejpam-3942	52	11	o1bc	o1bc	NUM
ejpam-3942	52	12	,	,	PUNCT
ejpam-3942	52	13	o1ac	o1ac	PROPN
ejpam-3942	52	14	,	,	PUNCT
ejpam-3942	52	15	o1ab	o1ab	PROPN
ejpam-3942	52	16	.	.	PUNCT
ejpam-3942	53	1	then	then	ADV
ejpam-3942	53	2	sabc	sabc	PROPN
ejpam-3942	53	3	=	=	PROPN
ejpam-3942	53	4	so1bc	so1bc	VERB
ejpam-3942	53	5	+	+	CCONJ
ejpam-3942	53	6	so1ac	so1ac	NOUN
ejpam-3942	53	7	−	−	NOUN
ejpam-3942	53	8	so1ab	so1ab	NOUN
ejpam-3942	53	9	=	=	SYM
ejpam-3942	53	10	1	1	NUM
ejpam-3942	53	11	2	2	NUM
ejpam-3942	53	12	bc	bc	PROPN
ejpam-3942	53	13	·	·	PUNCT
ejpam-3942	53	14	r1	r1	PROPN
ejpam-3942	53	15	+	+	CCONJ
ejpam-3942	53	16	1	1	NUM
ejpam-3942	53	17	2	2	NUM
ejpam-3942	53	18	ac	ac	PROPN
ejpam-3942	53	19	·	·	PUNCT
ejpam-3942	53	20	r1	r1	NOUN
ejpam-3942	53	21	−	−	NUM
ejpam-3942	53	22	1	1	NUM
ejpam-3942	53	23	2	2	NUM
ejpam-3942	53	24	ab	ab	PROPN
ejpam-3942	53	25	·	·	PUNCT
ejpam-3942	53	26	r1	r1	PROPN
ejpam-3942	53	27	.	.	PUNCT
ejpam-3942	54	1	hence	hence	ADV
ejpam-3942	54	2	we	we	PRON
ejpam-3942	54	3	have	have	VERB
ejpam-3942	54	4	2	2	NUM
ejpam-3942	54	5	·	·	SYM
ejpam-3942	54	6	84	84	NUM
ejpam-3942	54	7	=	=	SYM
ejpam-3942	54	8	r1	r1	PROPN
ejpam-3942	54	9	(	(	PUNCT
ejpam-3942	54	10	14	14	NUM
ejpam-3942	54	11	+	+	NOUN
ejpam-3942	54	12	13−	13−	NUM
ejpam-3942	54	13	15	15	NUM
ejpam-3942	54	14	)	)	PUNCT
ejpam-3942	54	15	or	or	CCONJ
ejpam-3942	54	16	r1	r1	NOUN
ejpam-3942	54	17	=	=	SYM
ejpam-3942	54	18	14	14	NUM
ejpam-3942	54	19	.	.	PUNCT
ejpam-3942	55	1	s.	s.	PROPN
ejpam-3942	55	2	j.aliyev	j.aliyev	PROPN
ejpam-3942	55	3	,	,	PUNCT
ejpam-3942	55	4	s.	s.	PROPN
ejpam-3942	55	5	m.aghazade	m.aghazade	PROPN
ejpam-3942	55	6	,	,	PUNCT
ejpam-3942	55	7	g.	g.	PROPN
ejpam-3942	55	8	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3942	55	9	/	/	SYM
ejpam-3942	55	10	eur	eur	PROPN
ejpam-3942	55	11	.	.	PUNCT
ejpam-3942	56	1	j.	j.	PROPN
ejpam-3942	56	2	pure	pure	PROPN
ejpam-3942	56	3	appl	appl	PROPN
ejpam-3942	56	4	.	.	PROPN
ejpam-3942	56	5	math	math	PROPN
ejpam-3942	56	6	,	,	PUNCT
ejpam-3942	56	7	14	14	NUM
ejpam-3942	56	8	(	(	PUNCT
ejpam-3942	56	9	2	2	NUM
ejpam-3942	56	10	)	)	PUNCT
ejpam-3942	56	11	(	(	PUNCT
ejpam-3942	56	12	2021	2021	NUM
ejpam-3942	56	13	)	)	PUNCT
ejpam-3942	56	14	,	,	PUNCT
ejpam-3942	56	15	601	601	NUM
ejpam-3942	56	16	-	-	SYM
ejpam-3942	56	17	607	607	NUM
ejpam-3942	56	18	604	604	NUM
ejpam-3942	56	19	figure	figure	NOUN
ejpam-3942	56	20	3	3	NUM
ejpam-3942	56	21	:	:	PUNCT
ejpam-3942	56	22	rectangle	rectangle	NOUN
ejpam-3942	56	23	abcd	abcd	NOUN
ejpam-3942	56	24	and	and	CCONJ
ejpam-3942	56	25	the	the	DET
ejpam-3942	56	26	inscribed	inscribe	VERB
ejpam-3942	56	27	rhombus	rhombus	NOUN
ejpam-3942	56	28	mnkp	mnkp	NOUN
ejpam-3942	56	29	.	.	PUNCT
ejpam-3942	57	1	similarly	similarly	ADV
ejpam-3942	57	2	we	we	PRON
ejpam-3942	57	3	find	find	VERB
ejpam-3942	57	4	r2	r2	PROPN
ejpam-3942	57	5	and	and	CCONJ
ejpam-3942	57	6	r3	r3	PROPN
ejpam-3942	57	7	:	:	PUNCT
ejpam-3942	57	8	sabc	sabc	PROPN
ejpam-3942	57	9	=	=	PROPN
ejpam-3942	57	10	so2bc	so2bc	PROPN
ejpam-3942	57	11	+	+	CCONJ
ejpam-3942	57	12	so2ab	so2ab	NUM
ejpam-3942	57	13	−	−	NOUN
ejpam-3942	57	14	so2ac	so2ac	NOUN
ejpam-3942	57	15	=	=	SYM
ejpam-3942	57	16	1	1	NUM
ejpam-3942	57	17	2	2	NUM
ejpam-3942	57	18	bc	bc	PROPN
ejpam-3942	57	19	·	·	PUNCT
ejpam-3942	57	20	r2	r2	PROPN
ejpam-3942	57	21	+	+	CCONJ
ejpam-3942	58	1	1	1	NUM
ejpam-3942	58	2	2	2	NUM
ejpam-3942	58	3	ab	ab	PROPN
ejpam-3942	58	4	·	·	PUNCT
ejpam-3942	58	5	r2	r2	PROPN
ejpam-3942	58	6	−	−	NOUN
ejpam-3942	58	7	1	1	NUM
ejpam-3942	58	8	2	2	NUM
ejpam-3942	58	9	ac	ac	PROPN
ejpam-3942	58	10	·	·	PUNCT
ejpam-3942	58	11	r2	r2	PROPN
ejpam-3942	58	12	,	,	PUNCT
ejpam-3942	58	13	2	2	NUM
ejpam-3942	58	14	·	·	SYM
ejpam-3942	58	15	84	84	NUM
ejpam-3942	58	16	=	=	SYM
ejpam-3942	58	17	r2	r2	PROPN
ejpam-3942	58	18	(	(	PUNCT
ejpam-3942	58	19	14	14	NUM
ejpam-3942	58	20	+	+	NUM
ejpam-3942	58	21	15−	15−	PROPN
ejpam-3942	58	22	13	13	NUM
ejpam-3942	58	23	)	)	PUNCT
ejpam-3942	58	24	or	or	CCONJ
ejpam-3942	58	25	r2	r2	NOUN
ejpam-3942	58	26	=	=	SYM
ejpam-3942	58	27	21	21	NUM
ejpam-3942	58	28	2	2	NUM
ejpam-3942	58	29	;	;	PUNCT
ejpam-3942	58	30	sabc	sabc	PROPN
ejpam-3942	58	31	=	=	PROPN
ejpam-3942	58	32	so3ab	so3ab	NOUN
ejpam-3942	58	33	+	+	CCONJ
ejpam-3942	58	34	so3ac	so3ac	NUM
ejpam-3942	58	35	−	−	NOUN
ejpam-3942	58	36	so3bc	so3bc	NUM
ejpam-3942	58	37	=	=	SYM
ejpam-3942	58	38	1	1	NUM
ejpam-3942	58	39	2	2	NUM
ejpam-3942	58	40	ab	ab	PROPN
ejpam-3942	58	41	·	·	PUNCT
ejpam-3942	58	42	r3	r3	PROPN
ejpam-3942	58	43	+	+	CCONJ
ejpam-3942	58	44	1	1	NUM
ejpam-3942	58	45	2	2	NUM
ejpam-3942	58	46	ac	ac	PROPN
ejpam-3942	58	47	·	·	PUNCT
ejpam-3942	58	48	r3	r3	PROPN
ejpam-3942	58	49	−	−	NOUN
ejpam-3942	58	50	1	1	NUM
ejpam-3942	58	51	2	2	NUM
ejpam-3942	58	52	bc	bc	PROPN
ejpam-3942	58	53	·	·	SYM
ejpam-3942	58	54	r3	r3	PROPN
ejpam-3942	58	55	,	,	PUNCT
ejpam-3942	58	56	2	2	NUM
ejpam-3942	58	57	·	·	SYM
ejpam-3942	58	58	84	84	NUM
ejpam-3942	58	59	=	=	SYM
ejpam-3942	58	60	r3	r3	PROPN
ejpam-3942	58	61	(	(	PUNCT
ejpam-3942	58	62	15	15	NUM
ejpam-3942	58	63	+	+	NOUN
ejpam-3942	58	64	13−	13−	NUM
ejpam-3942	58	65	14	14	NUM
ejpam-3942	58	66	)	)	PUNCT
ejpam-3942	58	67	or	or	CCONJ
ejpam-3942	58	68	r3	r3	PROPN
ejpam-3942	58	69	=	=	SYM
ejpam-3942	58	70	12	12	NUM
ejpam-3942	58	71	.	.	PUNCT
ejpam-3942	59	1	note	note	VERB
ejpam-3942	59	2	that	that	SCONJ
ejpam-3942	59	3	after	after	ADP
ejpam-3942	59	4	having	having	AUX
ejpam-3942	59	5	found	find	VERB
ejpam-3942	59	6	the	the	DET
ejpam-3942	59	7	radii	radii	NOUN
ejpam-3942	59	8	r	r	NOUN
ejpam-3942	59	9	,	,	PUNCT
ejpam-3942	59	10	r1	r1	NOUN
ejpam-3942	59	11	and	and	CCONJ
ejpam-3942	59	12	r2	r2	PROPN
ejpam-3942	59	13	,	,	PUNCT
ejpam-3942	59	14	we	we	PRON
ejpam-3942	59	15	could	could	AUX
ejpam-3942	59	16	also	also	ADV
ejpam-3942	59	17	find	find	VERB
ejpam-3942	59	18	the	the	DET
ejpam-3942	59	19	radius	radius	ADJ
ejpam-3942	59	20	r3	r3	PROPN
ejpam-3942	59	21	by	by	ADP
ejpam-3942	59	22	the	the	DET
ejpam-3942	59	23	well	well	ADV
ejpam-3942	59	24	-	-	PUNCT
ejpam-3942	59	25	known	know	VERB
ejpam-3942	59	26	formula	formula	NOUN
ejpam-3942	59	27	1	1	NUM
ejpam-3942	59	28	r	r	NOUN
ejpam-3942	59	29	=	=	SYM
ejpam-3942	59	30	1	1	NUM
ejpam-3942	59	31	r1	r1	NOUN
ejpam-3942	59	32	+	+	CCONJ
ejpam-3942	59	33	1	1	NUM
ejpam-3942	59	34	r2	r2	NOUN
ejpam-3942	59	35	+	+	CCONJ
ejpam-3942	59	36	1	1	NUM
ejpam-3942	59	37	r3	r3	PROPN
ejpam-3942	59	38	.	.	PUNCT
ejpam-3942	60	1	the	the	DET
ejpam-3942	60	2	area	area	NOUN
ejpam-3942	60	3	method	method	NOUN
ejpam-3942	60	4	obviously	obviously	ADV
ejpam-3942	60	5	makes	make	VERB
ejpam-3942	60	6	the	the	DET
ejpam-3942	60	7	solution	solution	NOUN
ejpam-3942	60	8	of	of	ADP
ejpam-3942	60	9	this	this	DET
ejpam-3942	60	10	problem	problem	NOUN
ejpam-3942	60	11	easier	easy	ADJ
ejpam-3942	60	12	as	as	SCONJ
ejpam-3942	60	13	the	the	DET
ejpam-3942	60	14	problem	problem	NOUN
ejpam-3942	60	15	becomes	become	VERB
ejpam-3942	60	16	less	less	ADV
ejpam-3942	60	17	complex	complex	ADJ
ejpam-3942	60	18	with	with	ADP
ejpam-3942	60	19	no	no	DET
ejpam-3942	60	20	need	need	NOUN
ejpam-3942	60	21	for	for	ADP
ejpam-3942	60	22	some	some	DET
ejpam-3942	60	23	logical	logical	ADJ
ejpam-3942	60	24	considerations	consideration	NOUN
ejpam-3942	60	25	.	.	PUNCT
ejpam-3942	61	1	moreover	moreover	ADV
ejpam-3942	61	2	,	,	PUNCT
ejpam-3942	61	3	a	a	DET
ejpam-3942	61	4	synthetic	synthetic	ADJ
ejpam-3942	61	5	and	and	CCONJ
ejpam-3942	61	6	technical	technical	ADJ
ejpam-3942	61	7	problem	problem	NOUN
ejpam-3942	61	8	becomes	become	VERB
ejpam-3942	61	9	a	a	DET
ejpam-3942	61	10	nice	nice	ADJ
ejpam-3942	61	11	one	one	NOUN
ejpam-3942	61	12	.	.	PUNCT
ejpam-3942	62	1	the	the	DET
ejpam-3942	62	2	area	area	NOUN
ejpam-3942	62	3	method	method	NOUN
ejpam-3942	62	4	is	be	AUX
ejpam-3942	62	5	one	one	NUM
ejpam-3942	62	6	of	of	ADP
ejpam-3942	62	7	those	those	PRON
ejpam-3942	62	8	which	which	PRON
ejpam-3942	62	9	helps	help	VERB
ejpam-3942	62	10	to	to	PART
ejpam-3942	62	11	find	find	VERB
ejpam-3942	62	12	nice	nice	ADJ
ejpam-3942	62	13	and	and	CCONJ
ejpam-3942	62	14	laconic	laconic	ADJ
ejpam-3942	62	15	solutions	solution	NOUN
ejpam-3942	62	16	for	for	ADP
ejpam-3942	62	17	different	different	ADJ
ejpam-3942	62	18	problems	problem	NOUN
ejpam-3942	62	19	.	.	PUNCT
ejpam-3942	63	1	being	be	AUX
ejpam-3942	63	2	internal	internal	ADJ
ejpam-3942	63	3	with	with	ADP
ejpam-3942	63	4	respect	respect	NOUN
ejpam-3942	63	5	to	to	ADP
ejpam-3942	63	6	geometry	geometry	NOUN
ejpam-3942	63	7	,	,	PUNCT
ejpam-3942	63	8	it	it	PRON
ejpam-3942	63	9	is	be	AUX
ejpam-3942	63	10	general	general	ADJ
ejpam-3942	63	11	for	for	ADP
ejpam-3942	63	12	problem	problem	NOUN
ejpam-3942	63	13	solving	solve	VERB
ejpam-3942	63	14	.	.	PUNCT
ejpam-3942	64	1	didactic	didactic	ADJ
ejpam-3942	64	2	importance	importance	NOUN
ejpam-3942	64	3	of	of	ADP
ejpam-3942	64	4	the	the	DET
ejpam-3942	64	5	area	area	NOUN
ejpam-3942	64	6	method	method	NOUN
ejpam-3942	64	7	is	be	AUX
ejpam-3942	64	8	that	that	SCONJ
ejpam-3942	64	9	it	it	PRON
ejpam-3942	64	10	is	be	AUX
ejpam-3942	64	11	a	a	DET
ejpam-3942	64	12	study	study	NOUN
ejpam-3942	64	13	subject	subject	NOUN
ejpam-3942	64	14	and	and	CCONJ
ejpam-3942	64	15	a	a	DET
ejpam-3942	64	16	tool	tool	NOUN
ejpam-3942	64	17	for	for	ADP
ejpam-3942	64	18	teaching	teach	VERB
ejpam-3942	64	19	the	the	DET
ejpam-3942	64	20	next	next	ADJ
ejpam-3942	64	21	lesson	lesson	NOUN
ejpam-3942	64	22	(	(	PUNCT
ejpam-3942	64	23	for	for	ADP
ejpam-3942	64	24	example	example	NOUN
ejpam-3942	64	25	,	,	PUNCT
ejpam-3942	64	26	the	the	DET
ejpam-3942	64	27	lesson	lesson	NOUN
ejpam-3942	64	28	entitled	entitle	VERB
ejpam-3942	64	29	similarity	similarity	NOUN
ejpam-3942	64	30	)	)	PUNCT
ejpam-3942	64	31	simultaneously	simultaneously	ADV
ejpam-3942	64	32	.	.	PUNCT
ejpam-3942	65	1	within	within	ADP
ejpam-3942	65	2	the	the	DET
ejpam-3942	65	3	framework	framework	NOUN
ejpam-3942	65	4	of	of	ADP
ejpam-3942	65	5	humanitarization	humanitarization	NOUN
ejpam-3942	65	6	of	of	ADP
ejpam-3942	65	7	the	the	DET
ejpam-3942	65	8	education	education	NOUN
ejpam-3942	65	9	,	,	PUNCT
ejpam-3942	65	10	this	this	DET
ejpam-3942	65	11	method	method	NOUN
ejpam-3942	65	12	is	be	AUX
ejpam-3942	65	13	of	of	ADP
ejpam-3942	65	14	great	great	ADJ
ejpam-3942	65	15	importance	importance	NOUN
ejpam-3942	65	16	from	from	ADP
ejpam-3942	65	17	cultural	cultural	ADJ
ejpam-3942	65	18	and	and	CCONJ
ejpam-3942	65	19	aesthetic	aesthetic	ADJ
ejpam-3942	65	20	aspects	aspect	NOUN
ejpam-3942	65	21	.	.	PUNCT
ejpam-3942	66	1	the	the	DET
ejpam-3942	66	2	use	use	NOUN
ejpam-3942	66	3	of	of	ADP
ejpam-3942	66	4	area	area	NOUN
ejpam-3942	66	5	method	method	NOUN
ejpam-3942	66	6	provides	provide	VERB
ejpam-3942	66	7	the	the	DET
ejpam-3942	66	8	possibility	possibility	NOUN
ejpam-3942	66	9	to	to	PART
ejpam-3942	66	10	develop	develop	VERB
ejpam-3942	66	11	interdisciplinary	interdisciplinary	ADJ
ejpam-3942	66	12	relationships	relationship	NOUN
ejpam-3942	66	13	:	:	PUNCT
ejpam-3942	66	14	some	some	DET
ejpam-3942	66	15	trigonometric	trigonometric	ADJ
ejpam-3942	66	16	formulas	formula	NOUN
ejpam-3942	66	17	are	be	AUX
ejpam-3942	66	18	easily	easily	ADV
ejpam-3942	66	19	proved	prove	VERB
ejpam-3942	66	20	by	by	ADP
ejpam-3942	66	21	this	this	DET
ejpam-3942	66	22	method	method	NOUN
ejpam-3942	66	23	.	.	PUNCT
ejpam-3942	67	1	lets	lets	AUX
ejpam-3942	67	2	give	give	VERB
ejpam-3942	67	3	a	a	DET
ejpam-3942	67	4	nice	nice	ADJ
ejpam-3942	67	5	example	example	NOUN
ejpam-3942	67	6	which	which	PRON
ejpam-3942	67	7	illustrates	illustrate	VERB
ejpam-3942	67	8	the	the	DET
ejpam-3942	67	9	possibility	possibility	NOUN
ejpam-3942	67	10	of	of	ADP
ejpam-3942	67	11	proving	prove	VERB
ejpam-3942	67	12	some	some	DET
ejpam-3942	67	13	trigonometric	trigonometric	ADJ
ejpam-3942	67	14	formulas	formula	NOUN
ejpam-3942	67	15	by	by	ADP
ejpam-3942	67	16	the	the	DET
ejpam-3942	67	17	area	area	NOUN
ejpam-3942	67	18	method	method	NOUN
ejpam-3942	67	19	.	.	PUNCT
ejpam-3942	68	1	consider	consider	VERB
ejpam-3942	68	2	the	the	DET
ejpam-3942	68	3	rectangle	rectangle	NOUN
ejpam-3942	68	4	abcd	abcd	NOUN
ejpam-3942	68	5	and	and	CCONJ
ejpam-3942	68	6	the	the	DET
ejpam-3942	68	7	rhombus	rhombus	NOUN
ejpam-3942	68	8	mnkp	mnkp	NOUN
ejpam-3942	68	9	inscribed	inscribe	VERB
ejpam-3942	68	10	in	in	ADP
ejpam-3942	68	11	abcd	abcd	PROPN
ejpam-3942	68	12	with	with	ADP
ejpam-3942	68	13	the	the	DET
ejpam-3942	68	14	sides	side	NOUN
ejpam-3942	68	15	equal	equal	ADJ
ejpam-3942	68	16	to	to	ADP
ejpam-3942	68	17	1	1	NUM
ejpam-3942	68	18	and	and	CCONJ
ejpam-3942	68	19	the	the	DET
ejpam-3942	68	20	angles	angles	NOUN
ejpam-3942	68	21	∠amp	∠amp	NOUN
ejpam-3942	69	1	=	=	PUNCT
ejpam-3942	69	2	α,∠pkd	α,∠pkd	NOUN
ejpam-3942	69	3	=	=	SYM
ejpam-3942	69	4	β	β	X
ejpam-3942	69	5	(	(	PUNCT
ejpam-3942	69	6	fig	fig	NOUN
ejpam-3942	69	7	.	.	PUNCT
ejpam-3942	69	8	3	3	NUM
ejpam-3942	69	9	)	)	PUNCT
ejpam-3942	69	10	.	.	PUNCT
ejpam-3942	70	1	the	the	DET
ejpam-3942	70	2	angle	angle	NOUN
ejpam-3942	70	3	at	at	ADP
ejpam-3942	70	4	the	the	DET
ejpam-3942	70	5	vertex	vertex	NOUN
ejpam-3942	70	6	p	p	NOUN
ejpam-3942	70	7	of	of	ADP
ejpam-3942	70	8	the	the	DET
ejpam-3942	70	9	rhombus	rhombus	NOUN
ejpam-3942	70	10	is	be	AUX
ejpam-3942	70	11	equal	equal	ADJ
ejpam-3942	70	12	to	to	ADP
ejpam-3942	70	13	α+β	α+β	PROPN
ejpam-3942	70	14	,	,	PUNCT
ejpam-3942	70	15	and	and	CCONJ
ejpam-3942	70	16	the	the	DET
ejpam-3942	70	17	area	area	NOUN
ejpam-3942	70	18	of	of	ADP
ejpam-3942	70	19	the	the	DET
ejpam-3942	70	20	rhombus	rhombus	NOUN
ejpam-3942	70	21	is	be	AUX
ejpam-3942	70	22	smnpk	smnpk	NOUN
ejpam-3942	70	23	=	=	PUNCT
ejpam-3942	70	24	sin	sin	NOUN
ejpam-3942	70	25	(	(	PUNCT
ejpam-3942	70	26	α+	α+	X
ejpam-3942	70	27	β	β	NOUN
ejpam-3942	70	28	)	)	PUNCT
ejpam-3942	70	29	.	.	PUNCT
ejpam-3942	71	1	s.	s.	PROPN
ejpam-3942	71	2	j.aliyev	j.aliyev	PROPN
ejpam-3942	71	3	,	,	PUNCT
ejpam-3942	71	4	s.	s.	PROPN
ejpam-3942	71	5	m.aghazade	m.aghazade	PROPN
ejpam-3942	71	6	,	,	PUNCT
ejpam-3942	71	7	g.	g.	PROPN
ejpam-3942	71	8	z.abdullayeva	z.abdullayeva	PROPN
ejpam-3942	71	9	/	/	SYM
ejpam-3942	71	10	eur	eur	PROPN
ejpam-3942	71	11	.	.	PUNCT
ejpam-3942	72	1	j.	j.	PROPN
ejpam-3942	72	2	pure	pure	PROPN
ejpam-3942	72	3	appl	appl	PROPN
ejpam-3942	72	4	.	.	PROPN
ejpam-3942	72	5	math	math	PROPN
ejpam-3942	72	6	,	,	PUNCT
ejpam-3942	72	7	14	14	NUM
ejpam-3942	72	8	(	(	PUNCT
ejpam-3942	72	9	2	2	NUM
ejpam-3942	72	10	)	)	PUNCT
ejpam-3942	72	11	(	(	PUNCT
ejpam-3942	72	12	2021	2021	NUM
ejpam-3942	72	13	)	)	PUNCT
ejpam-3942	72	14	,	,	PUNCT
ejpam-3942	72	15	601	601	NUM
ejpam-3942	72	16	-	-	SYM
ejpam-3942	72	17	607	607	NUM
ejpam-3942	72	18	605	605	NUM
ejpam-3942	72	19	figure	figure	NOUN
ejpam-3942	72	20	4	4	NUM
ejpam-3942	72	21	:	:	PUNCT
ejpam-3942	72	22	circle	circle	NOUN
ejpam-3942	72	23	centered	center	VERB
ejpam-3942	72	24	at	at	ADP
ejpam-3942	72	25	o	o	NOUN
ejpam-3942	72	26	with	with	ADP
ejpam-3942	72	27	diameter	diameter	PROPN
ejpam-3942	72	28	ab	ab	PROPN
ejpam-3942	72	29	.	.	PROPN
ejpam-3942	73	1	on	on	ADP
ejpam-3942	73	2	the	the	DET
ejpam-3942	73	3	other	other	ADJ
ejpam-3942	73	4	hand	hand	NOUN
ejpam-3942	73	5	,	,	PUNCT
ejpam-3942	73	6	the	the	DET
ejpam-3942	73	7	sides	side	NOUN
ejpam-3942	73	8	of	of	ADP
ejpam-3942	73	9	the	the	DET
ejpam-3942	73	10	rhombus	rhombus	NOUN
ejpam-3942	73	11	divide	divide	VERB
ejpam-3942	73	12	the	the	DET
ejpam-3942	73	13	rectangle	rectangle	NOUN
ejpam-3942	73	14	into	into	ADP
ejpam-3942	73	15	the	the	DET
ejpam-3942	73	16	pairs	pair	NOUN
ejpam-3942	73	17	of	of	ADP
ejpam-3942	73	18	equal	equal	ADJ
ejpam-3942	73	19	triangles	triangle	NOUN
ejpam-3942	73	20	amp	amp	NOUN
ejpam-3942	73	21	and	and	CCONJ
ejpam-3942	73	22	ckn	ckn	NOUN
ejpam-3942	73	23	,	,	PUNCT
ejpam-3942	73	24	bmn	bmn	NOUN
ejpam-3942	73	25	and	and	CCONJ
ejpam-3942	73	26	dkp	dkp	PROPN
ejpam-3942	73	27	,	,	PUNCT
ejpam-3942	73	28	with	with	ADP
ejpam-3942	73	29	catheti	catheti	ADJ
ejpam-3942	73	30	cosα	cosα	PROPN
ejpam-3942	73	31	,	,	PUNCT
ejpam-3942	73	32	sinα	sinα	PROPN
ejpam-3942	73	33	and	and	CCONJ
ejpam-3942	73	34	cosβ	cosβ	NOUN
ejpam-3942	73	35	,	,	PUNCT
ejpam-3942	73	36	sinβ	sinβ	NOUN
ejpam-3942	73	37	,	,	PUNCT
ejpam-3942	73	38	respectively	respectively	ADV
ejpam-3942	73	39	.	.	PUNCT
ejpam-3942	74	1	then	then	ADV
ejpam-3942	74	2	from	from	ADP
ejpam-3942	74	3	the	the	DET
ejpam-3942	74	4	obvious	obvious	ADJ
ejpam-3942	74	5	equality	equality	NOUN
ejpam-3942	74	6	smnkp	smnkp	NOUN
ejpam-3942	74	7	=	=	PRON
ejpam-3942	74	8	sabcd	sabcd	VERB
ejpam-3942	74	9	−	−	PROPN
ejpam-3942	74	10	2samp	2samp	NUM
ejpam-3942	75	1	−	−	PROPN
ejpam-3942	75	2	2sbmn	2sbmn	NUM
ejpam-3942	75	3	after	after	ADP
ejpam-3942	75	4	simplification	simplification	NOUN
ejpam-3942	75	5	we	we	PRON
ejpam-3942	75	6	have	have	VERB
ejpam-3942	75	7	smnkp	smnkp	NOUN
ejpam-3942	75	8	=	=	SYM
ejpam-3942	75	9	sinα	sinα	NOUN
ejpam-3942	75	10	cosβ	cosβ	NOUN
ejpam-3942	75	11	+	+	CCONJ
ejpam-3942	75	12	sinβ	sinβ	NOUN
ejpam-3942	75	13	cosα	cosα	PROPN
ejpam-3942	75	14	.	.	PUNCT
ejpam-3942	76	1	hence	hence	ADV
ejpam-3942	76	2	,	,	PUNCT
ejpam-3942	76	3	sin	sin	NOUN
ejpam-3942	76	4	(	(	PUNCT
ejpam-3942	76	5	α+	α+	X
ejpam-3942	76	6	β	β	X
ejpam-3942	76	7	)	)	PUNCT
ejpam-3942	76	8	=	=	SYM
ejpam-3942	76	9	sinα	sinα	NOUN
ejpam-3942	76	10	cosβ	cosβ	NOUN
ejpam-3942	76	11	+	+	CCONJ
ejpam-3942	76	12	sinβ	sinβ	NOUN
ejpam-3942	76	13	cosα	cosα	PROPN
ejpam-3942	76	14	.	.	PUNCT
ejpam-3942	77	1	the	the	DET
ejpam-3942	77	2	question	question	NOUN
ejpam-3942	77	3	arises	arise	VERB
ejpam-3942	77	4	when	when	SCONJ
ejpam-3942	77	5	solving	solve	VERB
ejpam-3942	77	6	problems	problem	NOUN
ejpam-3942	77	7	:	:	PUNCT
ejpam-3942	77	8	given	give	VERB
ejpam-3942	77	9	the	the	DET
ejpam-3942	77	10	problem	problem	NOUN
ejpam-3942	77	11	which	which	PRON
ejpam-3942	77	12	does	do	AUX
ejpam-3942	77	13	not	not	PART
ejpam-3942	77	14	involve	involve	VERB
ejpam-3942	77	15	the	the	DET
ejpam-3942	77	16	areas	area	NOUN
ejpam-3942	77	17	,	,	PUNCT
ejpam-3942	77	18	how	how	SCONJ
ejpam-3942	77	19	to	to	PART
ejpam-3942	77	20	determine	determine	VERB
ejpam-3942	77	21	whether	whether	SCONJ
ejpam-3942	77	22	it	it	PRON
ejpam-3942	77	23	will	will	AUX
ejpam-3942	77	24	be	be	AUX
ejpam-3942	77	25	useful	useful	ADJ
ejpam-3942	77	26	to	to	PART
ejpam-3942	77	27	apply	apply	VERB
ejpam-3942	77	28	the	the	DET
ejpam-3942	77	29	area	area	NOUN
ejpam-3942	77	30	method	method	NOUN
ejpam-3942	77	31	in	in	ADP
ejpam-3942	77	32	this	this	DET
ejpam-3942	77	33	case	case	NOUN
ejpam-3942	77	34	?	?	PUNCT
ejpam-3942	78	1	there	there	PRON
ejpam-3942	78	2	is	be	VERB
ejpam-3942	78	3	no	no	DET
ejpam-3942	78	4	general	general	ADJ
ejpam-3942	78	5	recommendations	recommendation	NOUN
ejpam-3942	78	6	for	for	ADP
ejpam-3942	78	7	this	this	DET
ejpam-3942	78	8	case	case	NOUN
ejpam-3942	78	9	,	,	PUNCT
ejpam-3942	78	10	but	but	CCONJ
ejpam-3942	78	11	the	the	DET
ejpam-3942	78	12	following	follow	VERB
ejpam-3942	78	13	tips	tip	NOUN
ejpam-3942	78	14	based	base	VERB
ejpam-3942	78	15	on	on	ADP
ejpam-3942	78	16	the	the	DET
ejpam-3942	78	17	analysis	analysis	NOUN
ejpam-3942	78	18	of	of	ADP
ejpam-3942	78	19	large	large	ADJ
ejpam-3942	78	20	number	number	NOUN
ejpam-3942	78	21	of	of	ADP
ejpam-3942	78	22	problems	problem	NOUN
ejpam-3942	78	23	solvable	solvable	ADJ
ejpam-3942	78	24	by	by	ADP
ejpam-3942	78	25	the	the	DET
ejpam-3942	78	26	area	area	NOUN
ejpam-3942	78	27	method	method	NOUN
ejpam-3942	78	28	may	may	AUX
ejpam-3942	78	29	be	be	AUX
ejpam-3942	78	30	very	very	ADV
ejpam-3942	78	31	useful	useful	ADJ
ejpam-3942	78	32	.	.	PUNCT
ejpam-3942	79	1	using	use	VERB
ejpam-3942	79	2	additive	additive	ADJ
ejpam-3942	79	3	property	property	NOUN
ejpam-3942	79	4	of	of	ADP
ejpam-3942	79	5	area	area	NOUN
ejpam-3942	79	6	will	will	AUX
ejpam-3942	79	7	most	most	ADV
ejpam-3942	79	8	likely	likely	ADV
ejpam-3942	79	9	help	help	VERB
ejpam-3942	79	10	to	to	PART
ejpam-3942	79	11	solve	solve	VERB
ejpam-3942	79	12	your	your	PRON
ejpam-3942	79	13	problem	problem	NOUN
ejpam-3942	79	14	by	by	ADP
ejpam-3942	79	15	the	the	DET
ejpam-3942	79	16	area	area	NOUN
ejpam-3942	79	17	method	method	NOUN
ejpam-3942	79	18	if	if	SCONJ
ejpam-3942	79	19	the	the	DET
ejpam-3942	79	20	problem	problem	NOUN
ejpam-3942	79	21	involves	involve	VERB
ejpam-3942	79	22	1	1	NUM
ejpam-3942	79	23	)	)	PUNCT
ejpam-3942	79	24	incircles	incircle	NOUN
ejpam-3942	79	25	and	and	CCONJ
ejpam-3942	79	26	excircles	excircle	NOUN
ejpam-3942	79	27	of	of	ADP
ejpam-3942	79	28	a	a	DET
ejpam-3942	79	29	triangle	triangle	NOUN
ejpam-3942	79	30	,	,	PUNCT
ejpam-3942	79	31	circles	circle	NOUN
ejpam-3942	79	32	tangent	tangent	ADJ
ejpam-3942	79	33	to	to	ADP
ejpam-3942	79	34	two	two	NUM
ejpam-3942	79	35	sides	side	NOUN
ejpam-3942	79	36	of	of	ADP
ejpam-3942	79	37	a	a	DET
ejpam-3942	79	38	triangle	triangle	NOUN
ejpam-3942	79	39	,	,	PUNCT
ejpam-3942	79	40	radius	radius	NOUN
ejpam-3942	79	41	,	,	PUNCT
ejpam-3942	79	42	angle	angle	NOUN
ejpam-3942	79	43	,	,	PUNCT
ejpam-3942	79	44	etc	etc	X
ejpam-3942	79	45	;	;	PUNCT
ejpam-3942	79	46	2	2	X
ejpam-3942	79	47	)	)	PUNCT
ejpam-3942	79	48	points	point	NOUN
ejpam-3942	79	49	lying	lie	VERB
ejpam-3942	79	50	on	on	ADP
ejpam-3942	79	51	the	the	DET
ejpam-3942	79	52	sides	side	NOUN
ejpam-3942	79	53	of	of	ADP
ejpam-3942	79	54	a	a	DET
ejpam-3942	79	55	polygon	polygon	NOUN
ejpam-3942	79	56	;	;	PUNCT
ejpam-3942	79	57	3	3	X
ejpam-3942	79	58	)	)	PUNCT
ejpam-3942	79	59	point	point	NOUN
ejpam-3942	79	60	inside	inside	ADP
ejpam-3942	79	61	a	a	DET
ejpam-3942	79	62	triangle	triangle	NOUN
ejpam-3942	79	63	which	which	PRON
ejpam-3942	79	64	divides	divide	VERB
ejpam-3942	79	65	it	it	PRON
ejpam-3942	79	66	into	into	ADP
ejpam-3942	79	67	several	several	ADJ
ejpam-3942	79	68	triangles	triangle	NOUN
ejpam-3942	79	69	,	,	PUNCT
ejpam-3942	79	70	projections	projection	NOUN
ejpam-3942	79	71	of	of	ADP
ejpam-3942	79	72	this	this	DET
ejpam-3942	79	73	point	point	NOUN
ejpam-3942	79	74	onto	onto	ADP
ejpam-3942	79	75	the	the	DET
ejpam-3942	79	76	sides	side	NOUN
ejpam-3942	79	77	of	of	ADP
ejpam-3942	79	78	a	a	DET
ejpam-3942	79	79	triangle	triangle	NOUN
ejpam-3942	79	80	;	;	PUNCT
ejpam-3942	79	81	4	4	X
ejpam-3942	79	82	)	)	PUNCT
ejpam-3942	79	83	proof	proof	NOUN
ejpam-3942	79	84	of	of	ADP
ejpam-3942	79	85	assertion	assertion	NOUN
ejpam-3942	79	86	that	that	SCONJ
ejpam-3942	79	87	three	three	NUM
ejpam-3942	79	88	points	point	NOUN
ejpam-3942	79	89	lie	lie	VERB
ejpam-3942	79	90	on	on	ADP
ejpam-3942	79	91	the	the	DET
ejpam-3942	79	92	same	same	ADJ
ejpam-3942	79	93	straight	straight	ADJ
ejpam-3942	79	94	line	line	NOUN
ejpam-3942	79	95	.	.	PUNCT
ejpam-3942	80	1	now	now	ADV
ejpam-3942	80	2	lets	lets	AUX
ejpam-3942	80	3	consider	consider	VERB
ejpam-3942	80	4	a	a	DET
ejpam-3942	80	5	problem	problem	NOUN
ejpam-3942	80	6	which	which	PRON
ejpam-3942	80	7	seems	seem	VERB
ejpam-3942	80	8	,	,	PUNCT
ejpam-3942	80	9	at	at	ADP
ejpam-3942	80	10	first	first	ADJ
ejpam-3942	80	11	glance	glance	NOUN
ejpam-3942	80	12	,	,	PUNCT
ejpam-3942	80	13	not	not	PART
ejpam-3942	80	14	related	relate	VERB
ejpam-3942	80	15	to	to	ADP
ejpam-3942	80	16	areas	area	NOUN
ejpam-3942	80	17	.	.	PUNCT
ejpam-3942	81	1	applying	apply	VERB
ejpam-3942	81	2	the	the	DET
ejpam-3942	81	3	area	area	NOUN
ejpam-3942	81	4	method	method	NOUN
ejpam-3942	81	5	to	to	ADP
ejpam-3942	81	6	this	this	DET
ejpam-3942	81	7	problem	problem	NOUN
ejpam-3942	81	8	significantly	significantly	ADV
ejpam-3942	81	9	facilitates	facilitate	VERB
ejpam-3942	81	10	its	its	PRON
ejpam-3942	81	11	solution	solution	NOUN
ejpam-3942	81	12	.	.	PUNCT
ejpam-3942	82	1	let	let	VERB
ejpam-3942	82	2	the	the	DET
ejpam-3942	82	3	point	point	NOUN
ejpam-3942	82	4	o	o	NOUN
ejpam-3942	82	5	be	be	AUX
ejpam-3942	82	6	the	the	DET
ejpam-3942	82	7	center	center	NOUN
ejpam-3942	82	8	of	of	ADP
ejpam-3942	82	9	the	the	DET
ejpam-3942	82	10	given	give	VERB
ejpam-3942	82	11	circle	circle	NOUN
ejpam-3942	82	12	,	,	PUNCT
ejpam-3942	82	13	nc	nc	PROPN
ejpam-3942	82	14	=	=	NOUN
ejpam-3942	82	15	kc	kc	PROPN
ejpam-3942	82	16	=	=	SYM
ejpam-3942	82	17	cp	cp	PROPN
ejpam-3942	82	18	,	,	PUNCT
ejpam-3942	82	19	kc⊥np	kc⊥np	NOUN
ejpam-3942	82	20	,	,	PUNCT
ejpam-3942	82	21	pm⊥ab	pm⊥ab	PROPN
ejpam-3942	82	22	,	,	PUNCT
ejpam-3942	82	23	an	an	DET
ejpam-3942	82	24	=	=	X
ejpam-3942	82	25	4,pm	4,pm	NOUN
ejpam-3942	82	26	=	=	SYM
ejpam-3942	82	27	4	4	NUM
ejpam-3942	82	28	,	,	PUNCT
ejpam-3942	82	29	8	8	NUM
ejpam-3942	82	30	(	(	PUNCT
ejpam-3942	82	31	fig	fig	NOUN
ejpam-3942	82	32	.	.	PUNCT
ejpam-3942	83	1	4	4	NUM
ejpam-3942	83	2	)	)	PUNCT
ejpam-3942	83	3	.	.	PUNCT
ejpam-3942	84	1	find	find	VERB
ejpam-3942	84	2	the	the	DET
ejpam-3942	84	3	radius	radius	NOUN
ejpam-3942	84	4	of	of	ADP
ejpam-3942	84	5	this	this	DET
ejpam-3942	84	6	circle	circle	NOUN
ejpam-3942	84	7	.	.	PUNCT
ejpam-3942	85	1	denote	denote	VERB
ejpam-3942	85	2	by	by	ADP
ejpam-3942	85	3	r	r	NOUN
ejpam-3942	85	4	the	the	DET
ejpam-3942	85	5	radius	radius	NOUN
ejpam-3942	85	6	of	of	ADP
ejpam-3942	85	7	this	this	DET
ejpam-3942	85	8	circle	circle	NOUN
ejpam-3942	85	9	.	.	PUNCT
ejpam-3942	86	1	as	as	ADP
ejpam-3942	86	2	nc	nc	PROPN
ejpam-3942	86	3	=	=	PROPN
ejpam-3942	86	4	kc	kc	PROPN
ejpam-3942	86	5	=	=	SYM
ejpam-3942	86	6	cp	cp	PROPN
ejpam-3942	86	7	,	,	PUNCT
ejpam-3942	86	8	the	the	DET
ejpam-3942	86	9	triangle	triangle	NOUN
ejpam-3942	86	10	pkn	pkn	PROPN
ejpam-3942	86	11	is	be	AUX
ejpam-3942	86	12	rectangular	rectangular	ADJ
ejpam-3942	86	13	and	and	CCONJ
ejpam-3942	86	14	∠pkn	∠pkn	NOUN
ejpam-3942	86	15	=	=	SYM
ejpam-3942	86	16	90	90	NUM
ejpam-3942	86	17	◦	◦	NOUN
ejpam-3942	86	18	.	.	PUNCT
ejpam-3942	87	1	from	from	ADP
ejpam-3942	87	2	kc⊥np	kc⊥np	NOUN
ejpam-3942	87	3	it	it	PRON
ejpam-3942	87	4	follows	follow	VERB
ejpam-3942	87	5	that	that	SCONJ
ejpam-3942	87	6	this	this	DET
ejpam-3942	87	7	rectangular	rectangular	ADJ
ejpam-3942	87	8	triangle	triangle	NOUN
ejpam-3942	87	9	pkn	pkn	PROPN
ejpam-3942	87	10	is	be	AUX
ejpam-3942	87	11	even	even	ADV
ejpam-3942	87	12	isosceles	isoscele	NOUN
ejpam-3942	87	13	:	:	PUNCT
ejpam-3942	87	14	pk	pk	NOUN
ejpam-3942	87	15	=	=	SYM
ejpam-3942	87	16	kn	kn	PROPN
ejpam-3942	87	17	.	.	PUNCT
ejpam-3942	88	1	let	let	VERB
ejpam-3942	88	2	ke	ke	NOUN
ejpam-3942	88	3	be	be	AUX
ejpam-3942	88	4	a	a	DET
ejpam-3942	88	5	chord	chord	NOUN
ejpam-3942	88	6	passing	pass	VERB
ejpam-3942	88	7	through	through	ADP
ejpam-3942	88	8	the	the	DET
ejpam-3942	88	9	point	point	NOUN
ejpam-3942	88	10	n	n	ADV
ejpam-3942	88	11	.	.	PUNCT
ejpam-3942	89	1	as	as	ADP
ejpam-3942	89	2	∠pkn	∠pkn	PROPN
ejpam-3942	89	3	=	=	SYM
ejpam-3942	89	4	90	90	NUM
ejpam-3942	89	5	◦	◦	NOUN
ejpam-3942	89	6	,	,	PUNCT
ejpam-3942	89	7	the	the	DET
ejpam-3942	89	8	interval	interval	NOUN
ejpam-3942	89	9	pe	pe	VERB
ejpam-3942	89	10	connecting	connect	VERB
ejpam-3942	89	11	the	the	DET
ejpam-3942	89	12	points	point	NOUN
ejpam-3942	89	13	p	p	NOUN
ejpam-3942	89	14	and	and	CCONJ
ejpam-3942	89	15	e	e	NOUN
ejpam-3942	89	16	passes	pass	VERB
ejpam-3942	89	17	through	through	ADP
ejpam-3942	89	18	the	the	DET
ejpam-3942	89	19	point	point	NOUN
ejpam-3942	89	20	o	o	NOUN
ejpam-3942	89	21	,	,	PUNCT
ejpam-3942	89	22	i.e.	i.e.	X
ejpam-3942	89	23	pe	pe	X
ejpam-3942	89	24	is	be	AUX
ejpam-3942	89	25	a	a	DET
ejpam-3942	89	26	diameter	diameter	NOUN
ejpam-3942	89	27	of	of	ADP
ejpam-3942	89	28	the	the	DET
ejpam-3942	89	29	circle	circle	NOUN
ejpam-3942	89	30	(	(	PUNCT
ejpam-3942	89	31	fig	fig	NOUN
ejpam-3942	89	32	.	.	PUNCT
ejpam-3942	89	33	5	5	NUM
ejpam-3942	89	34	)	)	PUNCT
ejpam-3942	89	35	.	.	PUNCT
ejpam-3942	90	1	references	reference	NOUN
ejpam-3942	90	2	606	606	NUM
ejpam-3942	90	3	figure	figure	NOUN
ejpam-3942	90	4	5	5	NUM
ejpam-3942	90	5	:	:	PUNCT
ejpam-3942	90	6	circumscribed	circumscribed	ADJ
ejpam-3942	90	7	circle	circle	NOUN
ejpam-3942	90	8	of	of	ADP
ejpam-3942	90	9	rectangular	rectangular	ADJ
ejpam-3942	90	10	triangle	triangle	NOUN
ejpam-3942	90	11	pke	pke	PROPN
ejpam-3942	90	12	.	.	PUNCT
ejpam-3942	91	1	by	by	ADP
ejpam-3942	91	2	intersecting	intersect	VERB
ejpam-3942	91	3	chords	chord	NOUN
ejpam-3942	91	4	theorem	theorem	VERB
ejpam-3942	91	5	we	we	PRON
ejpam-3942	91	6	have	have	VERB
ejpam-3942	91	7	kn	kn	PROPN
ejpam-3942	91	8	·	·	PUNCT
ejpam-3942	91	9	ne	ne	X
ejpam-3942	91	10	=	=	PUNCT
ejpam-3942	91	11	an	an	DET
ejpam-3942	91	12	·	·	PUNCT
ejpam-3942	91	13	nb	nb	NOUN
ejpam-3942	91	14	or	or	CCONJ
ejpam-3942	91	15	kn	kn	PROPN
ejpam-3942	91	16	·	·	PUNCT
ejpam-3942	91	17	ne	ne	X
ejpam-3942	91	18	=	=	SYM
ejpam-3942	91	19	4	4	NUM
ejpam-3942	91	20	(	(	PUNCT
ejpam-3942	91	21	2r−	2r−	PROPN
ejpam-3942	91	22	4	4	NUM
ejpam-3942	91	23	)	)	PUNCT
ejpam-3942	91	24	.	.	PUNCT
ejpam-3942	92	1	on	on	ADP
ejpam-3942	92	2	the	the	DET
ejpam-3942	92	3	other	other	ADJ
ejpam-3942	92	4	hand	hand	NOUN
ejpam-3942	92	5	,	,	PUNCT
ejpam-3942	92	6	as	as	ADP
ejpam-3942	92	7	snep	snep	NOUN
ejpam-3942	92	8	=	=	SYM
ejpam-3942	92	9	ne	ne	PROPN
ejpam-3942	92	10	·	·	PUNCT
ejpam-3942	92	11	kp	kp	X
ejpam-3942	92	12	2	2	NUM
ejpam-3942	92	13	=	=	SYM
ejpam-3942	92	14	kn	kn	PROPN
ejpam-3942	92	15	·	·	PUNCT
ejpam-3942	92	16	ne	ne	PROPN
ejpam-3942	92	17	2	2	NUM
ejpam-3942	92	18	=	=	SYM
ejpam-3942	92	19	2	2	NUM
ejpam-3942	92	20	(	(	PUNCT
ejpam-3942	92	21	2r−	2r−	PROPN
ejpam-3942	92	22	4	4	NUM
ejpam-3942	92	23	)	)	PUNCT
ejpam-3942	92	24	,	,	PUNCT
ejpam-3942	92	25	snop	snop	NOUN
ejpam-3942	92	26	=	=	PUNCT
ejpam-3942	92	27	no	no	PRON
ejpam-3942	92	28	·	·	SYM
ejpam-3942	92	29	4	4	NUM
ejpam-3942	92	30	,	,	PUNCT
ejpam-3942	92	31	8	8	NUM
ejpam-3942	92	32	2	2	NUM
ejpam-3942	92	33	=	=	SYM
ejpam-3942	92	34	2	2	NUM
ejpam-3942	92	35	,	,	PUNCT
ejpam-3942	92	36	4	4	NUM
ejpam-3942	92	37	(	(	PUNCT
ejpam-3942	92	38	r−	r−	NOUN
ejpam-3942	92	39	4	4	NUM
ejpam-3942	92	40	)	)	PUNCT
ejpam-3942	92	41	,	,	PUNCT
ejpam-3942	92	42	by	by	ADP
ejpam-3942	92	43	snep	snep	NOUN
ejpam-3942	92	44	=	=	SYM
ejpam-3942	92	45	2snop	2snop	NUM
ejpam-3942	92	46	we	we	PRON
ejpam-3942	92	47	have	have	AUX
ejpam-3942	92	48	2	2	NUM
ejpam-3942	92	49	(	(	PUNCT
ejpam-3942	92	50	2r−	2r−	PROPN
ejpam-3942	92	51	4	4	NUM
ejpam-3942	92	52	)	)	PUNCT
ejpam-3942	92	53	=	=	SYM
ejpam-3942	92	54	4	4	NUM
ejpam-3942	92	55	,	,	PUNCT
ejpam-3942	92	56	8	8	NUM
ejpam-3942	92	57	(	(	PUNCT
ejpam-3942	92	58	r−	r−	NOUN
ejpam-3942	92	59	4	4	NUM
ejpam-3942	92	60	)	)	PUNCT
ejpam-3942	92	61	or	or	CCONJ
ejpam-3942	92	62	r	r	NOUN
ejpam-3942	92	63	=	=	SYM
ejpam-3942	92	64	14	14	NUM
ejpam-3942	92	65	.	.	PUNCT
ejpam-3942	93	1	taking	take	VERB
ejpam-3942	93	2	into	into	ADP
ejpam-3942	93	3	consideration	consideration	NOUN
ejpam-3942	93	4	the	the	DET
ejpam-3942	93	5	results	result	NOUN
ejpam-3942	93	6	of	of	ADP
ejpam-3942	93	7	experimental	experimental	ADJ
ejpam-3942	93	8	research	research	NOUN
ejpam-3942	93	9	and	and	CCONJ
ejpam-3942	93	10	recommendations	recommendation	NOUN
ejpam-3942	93	11	by	by	ADP
ejpam-3942	93	12	the	the	DET
ejpam-3942	93	13	leading	lead	VERB
ejpam-3942	93	14	experts	expert	NOUN
ejpam-3942	93	15	and	and	CCONJ
ejpam-3942	93	16	teachers	teacher	NOUN
ejpam-3942	93	17	,	,	PUNCT
ejpam-3942	93	18	we	we	PRON
ejpam-3942	93	19	arrive	arrive	VERB
ejpam-3942	93	20	at	at	ADP
ejpam-3942	93	21	the	the	DET
ejpam-3942	93	22	conclusion	conclusion	NOUN
ejpam-3942	93	23	that	that	SCONJ
ejpam-3942	93	24	some	some	DET
ejpam-3942	93	25	changes	change	NOUN
ejpam-3942	93	26	to	to	ADP
ejpam-3942	93	27	secondary	secondary	ADJ
ejpam-3942	93	28	school	school	NOUN
ejpam-3942	93	29	geometry	geometry	NOUN
ejpam-3942	93	30	course	course	NOUN
ejpam-3942	93	31	,	,	PUNCT
ejpam-3942	93	32	in	in	ADP
ejpam-3942	93	33	other	other	ADJ
ejpam-3942	93	34	words	word	NOUN
ejpam-3942	93	35	,	,	PUNCT
ejpam-3942	93	36	the	the	DET
ejpam-3942	93	37	inclusion	inclusion	NOUN
ejpam-3942	93	38	of	of	ADP
ejpam-3942	93	39	the	the	DET
ejpam-3942	93	40	area	area	NOUN
ejpam-3942	93	41	method	method	NOUN
ejpam-3942	93	42	in	in	ADP
ejpam-3942	93	43	secondary	secondary	ADJ
ejpam-3942	93	44	school	school	NOUN
ejpam-3942	93	45	geometry	geometry	NOUN
ejpam-3942	93	46	course	course	NOUN
ejpam-3942	93	47	as	as	ADP
ejpam-3942	93	48	one	one	NUM
ejpam-3942	93	49	of	of	ADP
ejpam-3942	93	50	problem	problem	NOUN
ejpam-3942	93	51	solving	solving	NOUN
ejpam-3942	93	52	methods	method	NOUN
ejpam-3942	93	53	,	,	PUNCT
ejpam-3942	93	54	would	would	AUX
ejpam-3942	93	55	not	not	PART
ejpam-3942	93	56	only	only	ADV
ejpam-3942	93	57	enrich	enrich	VERB
ejpam-3942	93	58	students	student	NOUN
ejpam-3942	93	59	knowledge	knowledge	NOUN
ejpam-3942	93	60	,	,	PUNCT
ejpam-3942	93	61	but	but	CCONJ
ejpam-3942	93	62	would	would	AUX
ejpam-3942	93	63	also	also	ADV
ejpam-3942	93	64	contribute	contribute	VERB
ejpam-3942	93	65	to	to	ADP
ejpam-3942	93	66	further	further	ADJ
ejpam-3942	93	67	development	development	NOUN
ejpam-3942	93	68	of	of	ADP
ejpam-3942	93	69	geometry	geometry	NOUN
ejpam-3942	93	70	.	.	PUNCT
ejpam-3942	94	1	references	reference	NOUN
ejpam-3942	94	2	[	[	X
ejpam-3942	94	3	1	1	NUM
ejpam-3942	94	4	]	]	X
ejpam-3942	94	5	s.j.aliyev	s.j.aliyev	ADJ
ejpam-3942	94	6	,	,	PUNCT
ejpam-3942	94	7	s.n.efendi	s.n.efendi	NOUN
ejpam-3942	94	8	.	.	PUNCT
ejpam-3942	95	1	using	use	VERB
ejpam-3942	95	2	area	area	NOUN
ejpam-3942	95	3	method	method	NOUN
ejpam-3942	95	4	in	in	ADP
ejpam-3942	95	5	geometric	geometric	ADJ
ejpam-3942	95	6	problems	problem	NOUN
ejpam-3942	95	7	.	.	PUNCT
ejpam-3942	96	1	the	the	DET
ejpam-3942	96	2	way	way	NOUN
ejpam-3942	96	3	of	of	ADP
ejpam-3942	96	4	science	science	NOUN
ejpam-3942	96	5	,	,	PUNCT
ejpam-3942	96	6	international	international	ADJ
ejpam-3942	96	7	scientific	scientific	ADJ
ejpam-3942	96	8	journal	journal	NOUN
ejpam-3942	96	9	,	,	PUNCT
ejpam-3942	96	10	(	(	PUNCT
ejpam-3942	96	11	2016	2016	NUM
ejpam-3942	96	12	)	)	PUNCT
ejpam-3942	96	13	,	,	PUNCT
ejpam-3942	96	14	no4	no4	PROPN
ejpam-3942	96	15	,	,	PUNCT
ejpam-3942	96	16	(	(	PUNCT
ejpam-3942	96	17	26	26	NUM
ejpam-3942	96	18	)	)	PUNCT
ejpam-3942	96	19	,	,	PUNCT
ejpam-3942	96	20	p.15	p.15	PROPN
ejpam-3942	96	21	-	-	PUNCT
ejpam-3942	96	22	17	17	NUM
ejpam-3942	96	23	.	.	PUNCT
ejpam-3942	97	1	(	(	PUNCT
ejpam-3942	97	2	in	in	ADP
ejpam-3942	97	3	russian	russian	NOUN
ejpam-3942	97	4	)	)	PUNCT
ejpam-3942	98	1	[	[	X
ejpam-3942	98	2	2	2	NUM
ejpam-3942	98	3	]	]	X
ejpam-3942	98	4	i.a.kushnir	i.a.kushnir	ADJ
ejpam-3942	98	5	.	.	PUNCT
ejpam-3942	98	6	auxiliary	auxiliary	ADJ
ejpam-3942	98	7	element	element	NOUN
ejpam-3942	98	8	method	method	NOUN
ejpam-3942	98	9	.	.	PUNCT
ejpam-3942	99	1	kvant	kvant	PROPN
ejpam-3942	99	2	,	,	PUNCT
ejpam-3942	99	3	(	(	PUNCT
ejpam-3942	99	4	1974	1974	NUM
ejpam-3942	99	5	)	)	PUNCT
ejpam-3942	99	6	,	,	PUNCT
ejpam-3942	99	7	no2	no2	NOUN
ejpam-3942	99	8	,	,	PUNCT
ejpam-3942	99	9	p.46	p.46	PROPN
ejpam-3942	99	10	-	-	X
ejpam-3942	99	11	51	51	NUM
ejpam-3942	99	12	.	.	PUNCT
ejpam-3942	100	1	(	(	PUNCT
ejpam-3942	100	2	in	in	ADP
ejpam-3942	100	3	russian	russian	NOUN
ejpam-3942	100	4	)	)	PUNCT
ejpam-3942	101	1	[	[	X
ejpam-3942	101	2	3	3	NUM
ejpam-3942	101	3	]	]	PUNCT
ejpam-3942	101	4	i.d.novikov	i.d.novikov	NOUN
ejpam-3942	101	5	.	.	PUNCT
ejpam-3942	101	6	area	area	NOUN
ejpam-3942	101	7	method	method	NOUN
ejpam-3942	101	8	.	.	PUNCT
ejpam-3942	102	1	kvant	kvant	PROPN
ejpam-3942	102	2	,	,	PUNCT
ejpam-3942	102	3	(	(	PUNCT
ejpam-3942	102	4	1971	1971	NUM
ejpam-3942	102	5	)	)	PUNCT
ejpam-3942	102	6	,	,	PUNCT
ejpam-3942	102	7	no12	no12	PROPN
ejpam-3942	102	8	,	,	PUNCT
ejpam-3942	102	9	p.41	p.41	NOUN
ejpam-3942	102	10	-	-	SYM
ejpam-3942	102	11	46	46	NUM
ejpam-3942	102	12	.	.	PUNCT
ejpam-3942	103	1	(	(	PUNCT
ejpam-3942	103	2	in	in	ADP
ejpam-3942	103	3	russian	russian	NOUN
ejpam-3942	103	4	)	)	PUNCT
ejpam-3942	104	1	[	[	X
ejpam-3942	104	2	4	4	NUM
ejpam-3942	104	3	]	]	PUNCT
ejpam-3942	104	4	y.p.ponarin	y.p.ponarin	NOUN
ejpam-3942	104	5	.	.	PUNCT
ejpam-3942	104	6	elementary	elementary	PROPN
ejpam-3942	104	7	geometry	geometry	PROPN
ejpam-3942	104	8	.	.	PUNCT
ejpam-3942	105	1	vol	vol	NOUN
ejpam-3942	105	2	.	.	PROPN
ejpam-3942	106	1	1	1	NUM
ejpam-3942	106	2	,	,	PUNCT
ejpam-3942	106	3	msnmo	msnmo	NOUN
ejpam-3942	106	4	,	,	PUNCT
ejpam-3942	106	5	(	(	PUNCT
ejpam-3942	106	6	2008	2008	NUM
ejpam-3942	106	7	)	)	PUNCT
ejpam-3942	106	8	,	,	PUNCT
ejpam-3942	106	9	312	312	NUM
ejpam-3942	106	10	p.	p.	NOUN
ejpam-3942	106	11	(	(	PUNCT
ejpam-3942	106	12	in	in	ADP
ejpam-3942	106	13	russian	russian	NOUN
ejpam-3942	106	14	)	)	PUNCT
ejpam-3942	107	1	[	[	X
ejpam-3942	107	2	5	5	NUM
ejpam-3942	107	3	]	]	PUNCT
ejpam-3942	107	4	v.v.prasolov	v.v.prasolov	NOUN
ejpam-3942	107	5	.	.	PUNCT
ejpam-3942	108	1	using	use	VERB
ejpam-3942	108	2	the	the	DET
ejpam-3942	108	3	area	area	NOUN
ejpam-3942	108	4	.	.	PUNCT
ejpam-3942	109	1	kvant	kvant	ADJ
ejpam-3942	109	2	,	,	PUNCT
ejpam-3942	109	3	(	(	PUNCT
ejpam-3942	109	4	1986	1986	NUM
ejpam-3942	109	5	)	)	PUNCT
ejpam-3942	109	6	,	,	PUNCT
ejpam-3942	109	7	no5	no5	PROPN
ejpam-3942	109	8	,	,	PUNCT
ejpam-3942	109	9	p.16	p.16	PROPN
ejpam-3942	109	10	-	-	PROPN
ejpam-3942	109	11	19	19	NUM
ejpam-3942	109	12	.	.	PUNCT
ejpam-3942	110	1	(	(	PUNCT
ejpam-3942	110	2	in	in	ADP
ejpam-3942	110	3	russian	russian	ADJ
ejpam-3942	110	4	)	)	PUNCT
ejpam-3942	110	5	references	reference	VERB
ejpam-3942	110	6	607	607	NUM
ejpam-3942	110	7	[	[	X
ejpam-3942	110	8	6	6	NUM
ejpam-3942	110	9	]	]	PUNCT
ejpam-3942	110	10	e.g.gotman	e.g.gotman	NOUN
ejpam-3942	110	11	.	.	PUNCT
ejpam-3942	111	1	planimetry	planimetry	NOUN
ejpam-3942	111	2	problems	problem	NOUN
ejpam-3942	111	3	and	and	CCONJ
ejpam-3942	111	4	methods	method	NOUN
ejpam-3942	111	5	to	to	PART
ejpam-3942	111	6	solve	solve	VERB
ejpam-3942	111	7	them	they	PRON
ejpam-3942	111	8	.	.	PUNCT
ejpam-3942	112	1	prosvesheniye	prosvesheniye	PROPN
ejpam-3942	112	2	,	,	PUNCT
ejpam-3942	112	3	(	(	PUNCT
ejpam-3942	112	4	1996	1996	NUM
ejpam-3942	112	5	)	)	PUNCT
ejpam-3942	112	6	,	,	PUNCT
ejpam-3942	112	7	240	240	NUM
ejpam-3942	112	8	p.	p.	NOUN
ejpam-3942	112	9	(	(	PUNCT
ejpam-3942	112	10	in	in	ADP
ejpam-3942	112	11	russian	russian	NOUN
ejpam-3942	112	12	)	)	PUNCT
ejpam-3942	113	1	[	[	X
ejpam-3942	113	2	7	7	X
ejpam-3942	113	3	]	]	PUNCT
ejpam-3942	113	4	i.f.sharigin	i.f.sharigin	NOUN
ejpam-3942	113	5	.	.	PUNCT
ejpam-3942	114	1	learning	learn	VERB
ejpam-3942	114	2	to	to	PART
ejpam-3942	114	3	solve	solve	VERB
ejpam-3942	114	4	geometric	geometric	ADJ
ejpam-3942	114	5	problems	problem	NOUN
ejpam-3942	114	6	.	.	PUNCT
ejpam-3942	115	1	matematika	matematika	PROPN
ejpam-3942	115	2	v	v	PROPN
ejpam-3942	115	3	shkole	shkole	PROPN
ejpam-3942	115	4	,	,	PUNCT
ejpam-3942	115	5	(	(	PUNCT
ejpam-3942	115	6	1989	1989	NUM
ejpam-3942	115	7	)	)	PUNCT
ejpam-3942	115	8	,	,	PUNCT
ejpam-3942	115	9	no2	no2	NOUN
ejpam-3942	115	10	,	,	PUNCT
ejpam-3942	115	11	p.87	p.87	PROPN
ejpam-3942	115	12	-	-	X
ejpam-3942	115	13	101	101	NUM
ejpam-3942	115	14	.	.	PUNCT
ejpam-3942	116	1	(	(	PUNCT
ejpam-3942	116	2	in	in	ADP
ejpam-3942	116	3	russian	russian	NOUN
ejpam-3942	116	4	)	)	PUNCT