id	sid	tid	token	lemma	pos
ajird-807	1	1	american	american	PROPN
ajird-807	1	2	journal	journal	PROPN
ajird-807	1	3	of	of	ADP
ajird-807	1	4	interdisciplinary	interdisciplinary	ADJ
ajird-807	1	5	research	research	NOUN
ajird-807	1	6	and	and	CCONJ
ajird-807	1	7	development	development	NOUN
ajird-807	1	8	issn	issn	PROPN
ajird-807	1	9	online	online	NOUN
ajird-807	1	10	:	:	PUNCT
ajird-807	1	11	2771	2771	NUM
ajird-807	1	12	-	-	SYM
ajird-807	1	13	8948	8948	NUM
ajird-807	1	14	website	website	NOUN
ajird-807	1	15	:	:	PUNCT
ajird-807	1	16	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-807	1	17	volume	volume	NOUN
ajird-807	1	18	21	21	NUM
ajird-807	1	19	,	,	PUNCT
ajird-807	1	20	october	october	PROPN
ajird-807	1	21	,	,	PUNCT
ajird-807	1	22	2023	2023	NUM
ajird-807	1	23	152	152	NUM
ajird-807	2	1	|	|	ADV
ajird-807	2	2	p	p	NOUN
ajird-807	2	3	a	a	DET
ajird-807	2	4	g	g	NOUN
ajird-807	2	5	e	e	NOUN
ajird-807	2	6	problems	problem	NOUN
ajird-807	2	7	about	about	ADP
ajird-807	2	8	the	the	DET
ajird-807	2	9	largest	large	ADJ
ajird-807	2	10	and	and	CCONJ
ajird-807	2	11	smallest	small	ADJ
ajird-807	2	12	values	value	NOUN
ajird-807	2	13	in	in	ADP
ajird-807	2	14	circles	circle	NOUN
ajird-807	2	15	and	and	CCONJ
ajird-807	2	16	circles	circle	NOUN
ajird-807	2	17	khudaybergenova	khudaybergenova	PROPN
ajird-807	2	18	gulrabo	gulrabo	PROPN
ajird-807	2	19	komiljanovna	komiljanovna	PROPN
ajird-807	2	20	teacher	teacher	NOUN
ajird-807	2	21	of	of	ADP
ajird-807	2	22	the	the	DET
ajird-807	2	23	"	"	PUNCT
ajird-807	2	24	mathematical	mathematical	ADJ
ajird-807	2	25	analysis	analysis	NOUN
ajird-807	2	26	"	"	PUNCT
ajird-807	2	27	department	department	NOUN
ajird-807	2	28	of	of	ADP
ajird-807	2	29	the	the	DET
ajird-807	2	30	faculty	faculty	NOUN
ajird-807	2	31	of	of	ADP
ajird-807	2	32	physics	physics	NOUN
ajird-807	2	33	and	and	CCONJ
ajird-807	2	34	mathematics	mathematics	PROPN
ajird-807	2	35	of	of	ADP
ajird-807	2	36	urdu	urdu	PROPN
ajird-807	2	37	abstract	abstract	ADJ
ajird-807	2	38	this	this	DET
ajird-807	2	39	article	article	NOUN
ajird-807	2	40	provides	provide	VERB
ajird-807	2	41	solutions	solution	NOUN
ajird-807	2	42	to	to	ADP
ajird-807	2	43	some	some	DET
ajird-807	2	44	common	common	ADJ
ajird-807	2	45	problems	problem	NOUN
ajird-807	2	46	related	relate	VERB
ajird-807	2	47	to	to	ADP
ajird-807	2	48	circles	circle	NOUN
ajird-807	2	49	and	and	CCONJ
ajird-807	2	50	circles	circle	NOUN
ajird-807	2	51	.	.	PUNCT
ajird-807	3	1	through	through	ADP
ajird-807	3	2	these	these	PRON
ajird-807	3	3	,	,	PUNCT
ajird-807	3	4	the	the	DET
ajird-807	3	5	student	student	NOUN
ajird-807	3	6	learns	learn	VERB
ajird-807	3	7	that	that	SCONJ
ajird-807	3	8	he	he	PRON
ajird-807	3	9	can	can	AUX
ajird-807	3	10	solve	solve	VERB
ajird-807	3	11	problems	problem	NOUN
ajird-807	3	12	not	not	PART
ajird-807	3	13	in	in	ADP
ajird-807	3	14	the	the	DET
ajird-807	3	15	same	same	ADJ
ajird-807	3	16	way	way	NOUN
ajird-807	3	17	,	,	PUNCT
ajird-807	3	18	but	but	CCONJ
ajird-807	3	19	also	also	ADV
ajird-807	3	20	through	through	ADP
ajird-807	3	21	different	different	ADJ
ajird-807	3	22	creative	creative	ADJ
ajird-807	3	23	thinking	thinking	NOUN
ajird-807	3	24	.	.	PUNCT
ajird-807	4	1	keywords	keyword	NOUN
ajird-807	4	2	:	:	PUNCT
ajird-807	4	3	circle	circle	NOUN
ajird-807	4	4	,	,	PUNCT
ajird-807	4	5	volume	volume	NOUN
ajird-807	4	6	,	,	PUNCT
ajird-807	4	7	proof	proof	NOUN
ajird-807	4	8	,	,	PUNCT
ajird-807	4	9	theorem	theorem	NOUN
ajird-807	4	10	of	of	ADP
ajird-807	4	11	cosines	cosine	NOUN
ajird-807	4	12	,	,	PUNCT
ajird-807	4	13	perimeter	perimeter	NOUN
ajird-807	4	14	,	,	PUNCT
ajird-807	4	15	bisector	bisector	NOUN
ajird-807	4	16	,	,	PUNCT
ajird-807	4	17	angle	angle	NOUN
ajird-807	4	18	,	,	PUNCT
ajird-807	4	19	interior	interior	ADJ
ajird-807	4	20	angle	angle	NOUN
ajird-807	4	21	.	.	PUNCT
ajird-807	5	1	kirish	kirish	ADJ
ajird-807	5	2	issue	issue	NOUN
ajird-807	5	3	1	1	NUM
ajird-807	5	4	.	.	PUNCT
ajird-807	5	5	of	of	ADP
ajird-807	5	6	all	all	DET
ajird-807	5	7	the	the	DET
ajird-807	5	8	triangles	triangle	NOUN
ajird-807	5	9	inscribed	inscribe	VERB
ajird-807	5	10	in	in	ADP
ajird-807	5	11	a	a	DET
ajird-807	5	12	circle	circle	NOUN
ajird-807	5	13	,	,	PUNCT
ajird-807	5	14	find	find	VERB
ajird-807	5	15	the	the	DET
ajird-807	5	16	smallest	small	ADJ
ajird-807	5	17	sum	sum	NOUN
ajird-807	5	18	of	of	ADP
ajird-807	5	19	the	the	DET
ajird-807	5	20	squares	square	NOUN
ajird-807	5	21	of	of	ADP
ajird-807	5	22	the	the	DET
ajird-807	5	23	distances	distance	NOUN
ajird-807	5	24	from	from	ADP
ajird-807	5	25	the	the	DET
ajird-807	5	26	center	center	NOUN
ajird-807	5	27	of	of	ADP
ajird-807	5	28	the	the	DET
ajird-807	5	29	circle	circle	NOUN
ajird-807	5	30	to	to	ADP
ajird-807	5	31	the	the	DET
ajird-807	5	32	sides	side	NOUN
ajird-807	5	33	of	of	ADP
ajird-807	5	34	the	the	DET
ajird-807	5	35	triangle	triangle	NOUN
ajird-807	5	36	.	.	PUNCT
ajird-807	6	1	solution	solution	NOUN
ajird-807	6	2	:	:	PUNCT
ajird-807	6	3	abc	abc	PROPN
ajird-807	6	4	–	–	PUNCT
ajird-807	6	5	the	the	DET
ajird-807	6	6	desired	desire	VERB
ajird-807	6	7	triangle	triangle	NOUN
ajird-807	6	8	,	,	PUNCT
ajird-807	6	9	,	,	PUNCT
ajird-807	6	10	,	,	PUNCT
ajird-807	6	11	a	a	DET
ajird-807	6	12	b	b	NOUN
ajird-807	6	13	c	c	NOUN
ajird-807	6	14	sides	side	NOUN
ajird-807	6	15	,	,	PUNCT
ajird-807	6	16	distances	distance	NOUN
ajird-807	6	17	from	from	ADP
ajird-807	6	18	the	the	DET
ajird-807	6	19	center	center	NOUN
ajird-807	6	20	of	of	ADP
ajird-807	6	21	the	the	DET
ajird-807	6	22	outer	outer	ADJ
ajird-807	6	23	circle	circle	NOUN
ajird-807	6	24	to	to	ADP
ajird-807	6	25	the	the	DET
ajird-807	6	26	sides	side	NOUN
ajird-807	6	27	of	of	ADP
ajird-807	6	28	the	the	DET
ajird-807	6	29	triangle	triangle	NOUN
ajird-807	6	30	,	,	PUNCT
ajird-807	6	31	r	r	NOUN
ajird-807	6	32	the	the	DET
ajird-807	6	33	radius	radius	NOUN
ajird-807	6	34	of	of	ADP
ajird-807	6	35	the	the	DET
ajird-807	6	36	outer	outer	ADJ
ajird-807	6	37	circle	circle	NOUN
ajird-807	6	38	.	.	PUNCT
ajird-807	7	1	cos	cos	PROPN
ajird-807	7	2	,	,	PUNCT
ajird-807	7	3	cos	cos	PROPN
ajird-807	7	4	,	,	PUNCT
ajird-807	7	5	cosx	cosx	PROPN
ajird-807	7	6	r	r	PROPN
ajird-807	7	7	a	a	DET
ajird-807	7	8	y	y	NOUN
ajird-807	7	9	r	r	NOUN
ajird-807	7	10	b	b	PROPN
ajird-807	7	11	z	z	NOUN
ajird-807	7	12	r	r	NOUN
ajird-807	7	13	c=	c=	NOUN
ajird-807	8	1	=	=	NOUN
ajird-807	8	2	=	=	PUNCT
ajird-807	8	3	we	we	PRON
ajird-807	8	4	have	have	VERB
ajird-807	8	5	2	2	NUM
ajird-807	8	6	2	2	NUM
ajird-807	8	7	2	2	NUM
ajird-807	8	8	2	2	NUM
ajird-807	8	9	2	2	NUM
ajird-807	8	10	2	2	NUM
ajird-807	8	11	2	2	NUM
ajird-807	8	12	2	2	NUM
ajird-807	8	13	2	2	NUM
ajird-807	8	14	2	2	NUM
ajird-807	8	15	2(cos	2(cos	NUM
ajird-807	8	16	cos	cos	X
ajird-807	8	17	cos	cos	PROPN
ajird-807	8	18	)	)	PUNCT
ajird-807	8	19	(	(	PUNCT
ajird-807	8	20	3	3	NUM
ajird-807	8	21	(	(	PUNCT
ajird-807	8	22	sin	sin	NOUN
ajird-807	8	23	sin	sin	NOUN
ajird-807	8	24	sin	sin	NOUN
ajird-807	8	25	)	)	PUNCT
ajird-807	8	26	)	)	PUNCT
ajird-807	8	27	x	x	PUNCT
ajird-807	9	1	y	y	PROPN
ajird-807	9	2	z	z	NOUN
ajird-807	9	3	r	r	NOUN
ajird-807	9	4	a	a	DET
ajird-807	9	5	b	b	NOUN
ajird-807	9	6	c	c	NOUN
ajird-807	9	7	r	r	NOUN
ajird-807	9	8	a	a	DET
ajird-807	9	9	b	b	NOUN
ajird-807	9	10	c+	c+	NOUN
ajird-807	9	11	+	+	PUNCT
ajird-807	9	12	=	=	PUNCT
ajird-807	10	1	+	+	PUNCT
ajird-807	10	2	+	+	CCONJ
ajird-807	10	3	=	=	SYM
ajird-807	11	1	+	+	PUNCT
ajird-807	12	1	+	+	CCONJ
ajird-807	12	2	=	=	SYM
ajird-807	12	3	2	2	NUM
ajird-807	12	4	2	2	NUM
ajird-807	12	5	2	2	NUM
ajird-807	12	6	2	2	NUM
ajird-807	12	7	23	23	NUM
ajird-807	12	8	(	(	PUNCT
ajird-807	12	9	sin	sin	NOUN
ajird-807	12	10	sin	sin	NOUN
ajird-807	12	11	sin	sin	NOUN
ajird-807	12	12	(	(	PUNCT
ajird-807	12	13	)	)	PUNCT
ajird-807	12	14	)	)	PUNCT
ajird-807	12	15	r	r	NOUN
ajird-807	12	16	r	r	NOUN
ajird-807	12	17	a	a	DET
ajird-807	12	18	b	b	NOUN
ajird-807	12	19	a	a	DET
ajird-807	12	20	b=	b=	NOUN
ajird-807	12	21	+	+	X
ajird-807	13	1	+	+	CCONJ
ajird-807	13	2	+	+	CCONJ
ajird-807	13	3	let	let	VERB
ajird-807	13	4	's	us	PRON
ajird-807	13	5	look	look	VERB
ajird-807	13	6	at	at	ADP
ajird-807	13	7	the	the	DET
ajird-807	13	8	total	total	NOUN
ajird-807	13	9	.	.	PUNCT
ajird-807	14	1	of	of	ADP
ajird-807	14	2	course	course	NOUN
ajird-807	14	3	,	,	PUNCT
ajird-807	14	4	2	2	NUM
ajird-807	14	5	2	2	NUM
ajird-807	14	6	2x	2x	NUM
ajird-807	14	7	y	y	PROPN
ajird-807	14	8	z+	z+	NUM
ajird-807	14	9	+	+	CCONJ
ajird-807	14	10	collected	collect	VERB
ajird-807	14	11	,	,	PUNCT
ajird-807	14	12	2	2	NUM
ajird-807	14	13	2	2	NUM
ajird-807	14	14	2sin	2sin	NUM
ajird-807	14	15	sin	sin	NOUN
ajird-807	14	16	sin	sin	NOUN
ajird-807	14	17	(	(	PUNCT
ajird-807	14	18	)	)	PUNCT
ajird-807	14	19	a	a	DET
ajird-807	14	20	b	b	NOUN
ajird-807	14	21	a	a	DET
ajird-807	14	22	b+	b+	ADJ
ajird-807	14	23	+	+	CCONJ
ajird-807	14	24	+	+	CCONJ
ajird-807	14	25	is	be	AUX
ajird-807	14	26	the	the	DET
ajird-807	14	27	smallest	small	ADJ
ajird-807	14	28	when	when	SCONJ
ajird-807	14	29	the	the	DET
ajird-807	14	30	expression	expression	NOUN
ajird-807	14	31	takes	take	VERB
ajird-807	14	32	the	the	DET
ajird-807	14	33	largest	large	ADJ
ajird-807	14	34	value	value	NOUN
ajird-807	14	35	.	.	PUNCT
ajird-807	15	1	we	we	PRON
ajird-807	15	2	perform	perform	VERB
ajird-807	15	3	the	the	DET
ajird-807	15	4	following	follow	VERB
ajird-807	15	5	form	form	NOUN
ajird-807	15	6	substitutions	substitution	NOUN
ajird-807	15	7	:	:	PUNCT
ajird-807	15	8	2	2	NUM
ajird-807	15	9	2	2	NUM
ajird-807	15	10	2	2	NUM
ajird-807	15	11	2	2	NUM
ajird-807	15	12	2	2	NUM
ajird-807	15	13	2	2	NUM
ajird-807	15	14	2	2	NUM
ajird-807	15	15	2	2	NUM
ajird-807	15	16	1	1	NUM
ajird-807	15	17	cos2	cos2	NOUN
ajird-807	15	18	1	1	NUM
ajird-807	15	19	cos2	cos2	NOUN
ajird-807	15	20	sin	sin	VERB
ajird-807	15	21	sin	sin	NOUN
ajird-807	15	22	sin	sin	NOUN
ajird-807	15	23	(	(	PUNCT
ajird-807	15	24	)	)	PUNCT
ajird-807	15	25	1	1	NUM
ajird-807	15	26	cos	cos	PROPN
ajird-807	15	27	(	(	PUNCT
ajird-807	15	28	)	)	PUNCT
ajird-807	15	29	2	2	NUM
ajird-807	15	30	2	2	NUM
ajird-807	15	31	4	4	NUM
ajird-807	15	32	cos2	cos2	NOUN
ajird-807	15	33	cos2	cos2	PROPN
ajird-807	15	34	2	2	NUM
ajird-807	15	35	cos	cos	PROPN
ajird-807	15	36	(	(	PUNCT
ajird-807	15	37	)	)	PUNCT
ajird-807	15	38	2	2	NUM
ajird-807	15	39	(	(	PUNCT
ajird-807	15	40	cos	cos	PROPN
ajird-807	15	41	(	(	PUNCT
ajird-807	15	42	)	)	PUNCT
ajird-807	15	43	cos	cos	PROPN
ajird-807	15	44	(	(	PUNCT
ajird-807	15	45	)	)	PUNCT
ajird-807	15	46	cos	cos	PROPN
ajird-807	15	47	(	(	PUNCT
ajird-807	15	48	)	)	PUNCT
ajird-807	15	49	)	)	PUNCT
ajird-807	15	50	2	2	NUM
ajird-807	15	51	1	1	NUM
ajird-807	15	52	1	1	NUM
ajird-807	15	53	2	2	NUM
ajird-807	15	54	(	(	PUNCT
ajird-807	15	55	cos	cos	PROPN
ajird-807	15	56	(	(	PUNCT
ajird-807	15	57	)	)	PUNCT
ajird-807	15	58	cos	cos	PROPN
ajird-807	15	59	(	(	PUNCT
ajird-807	15	60	)	)	PUNCT
ajird-807	15	61	)	)	PUNCT
ajird-807	16	1	cos	cos	PROPN
ajird-807	16	2	(	(	PUNCT
ajird-807	16	3	)	)	PUNCT
ajird-807	16	4	.	.	PUNCT
ajird-807	17	1	2	2	NUM
ajird-807	17	2	4	4	NUM
ajird-807	17	3	a	a	DET
ajird-807	17	4	b	b	NOUN
ajird-807	17	5	a	a	DET
ajird-807	17	6	b	b	NOUN
ajird-807	17	7	a	a	DET
ajird-807	17	8	b	b	NOUN
ajird-807	17	9	a	a	DET
ajird-807	17	10	b	b	NOUN
ajird-807	17	11	a	a	DET
ajird-807	17	12	b	b	NOUN
ajird-807	17	13	a	a	DET
ajird-807	17	14	b	b	NOUN
ajird-807	17	15	a	a	DET
ajird-807	17	16	b	b	NOUN
ajird-807	17	17	a	a	DET
ajird-807	17	18	b	b	NOUN
ajird-807	17	19	a	a	DET
ajird-807	17	20	b	b	NOUN
ajird-807	17	21	a	a	DET
ajird-807	17	22	b	b	NOUN
ajird-807	17	23	a	a	DET
ajird-807	17	24	b	b	NOUN
ajird-807	17	25	a	a	DET
ajird-807	17	26	b	b	NOUN
ajird-807	17	27	+	+	CCONJ
ajird-807	17	28	+	+	PUNCT
ajird-807	17	29	+	+	CCONJ
ajird-807	17	30	=	=	X
ajird-807	18	1	+	+	PUNCT
ajird-807	19	1	+	+	PUNCT
ajird-807	19	2	+	+	PUNCT
ajird-807	19	3	=	=	SYM
ajird-807	19	4	+	+	NUM
ajird-807	19	5	=	=	SYM
ajird-807	19	6	=	=	PUNCT
ajird-807	19	7	+	+	NUM
ajird-807	19	8	×	×	NOUN
ajird-807	19	9	+	+	X
ajird-807	19	10	+	+	PUNCT
ajird-807	19	11	=	=	SYM
ajird-807	19	12	=	=	X
ajird-807	20	1	+	+	PUNCT
ajird-807	20	2	+	+	CCONJ
ajird-807	20	3	+	+	X
ajird-807	20	4	from	from	ADP
ajird-807	20	5	this	this	DET
ajird-807	20	6	2	2	NUM
ajird-807	20	7	2	2	NUM
ajird-807	20	8	2sin	2sin	NUM
ajird-807	20	9	sin	sin	NOUN
ajird-807	20	10	sin	sin	NOUN
ajird-807	20	11	(	(	PUNCT
ajird-807	20	12	)	)	PUNCT
ajird-807	20	13	a	a	DET
ajird-807	20	14	b	b	NOUN
ajird-807	20	15	a	a	DET
ajird-807	20	16	b+	b+	ADJ
ajird-807	20	17	+	+	X
ajird-807	20	18	+	+	CCONJ
ajird-807	20	19	for	for	ADP
ajird-807	20	20	the	the	DET
ajird-807	20	21	expression	expression	NOUN
ajird-807	20	22	to	to	PART
ajird-807	20	23	reach	reach	VERB
ajird-807	20	24	its	its	PRON
ajird-807	20	25	greatest	great	ADJ
ajird-807	20	26	value	value	NOUN
ajird-807	20	27	,	,	PUNCT
ajird-807	20	28	2cos	2cos	PROPN
ajird-807	20	29	(	(	PUNCT
ajird-807	20	30	)	)	PUNCT
ajird-807	20	31	a	a	DET
ajird-807	20	32	b	b	NOUN
ajird-807	20	33	it	it	PRON
ajird-807	20	34	follows	follow	VERB
ajird-807	20	35	that	that	SCONJ
ajird-807	20	36	it	it	PRON
ajird-807	20	37	is	be	AUX
ajird-807	20	38	necessary	necessary	ADJ
ajird-807	20	39	to	to	PART
ajird-807	20	40	take	take	VERB
ajird-807	20	41	the	the	DET
ajird-807	20	42	largest	large	ADJ
ajird-807	20	43	value	value	NOUN
ajird-807	20	44	,	,	PUNCT
ajird-807	20	45	i.e	i.e	PROPN
ajird-807	20	46	cos	cos	PROPN
ajird-807	20	47	(	(	PUNCT
ajird-807	20	48	)	)	PUNCT
ajird-807	20	49	1a	1a	PROPN
ajird-807	20	50	b=	b=	NOUN
ajird-807	20	51	from	from	ADP
ajird-807	20	52	that	that	DET
ajird-807	20	53	21	21	NUM
ajird-807	20	54	(	(	PUNCT
ajird-807	20	55	cos	cos	PROPN
ajird-807	20	56	(	(	PUNCT
ajird-807	20	57	)	)	PUNCT
ajird-807	20	58	cos	cos	PROPN
ajird-807	20	59	(	(	PUNCT
ajird-807	20	60	)	)	PUNCT
ajird-807	20	61	)	)	PUNCT
ajird-807	20	62	2	2	NUM
ajird-807	20	63	a	a	DET
ajird-807	20	64	b	b	NOUN
ajird-807	20	65	a	a	DET
ajird-807	20	66	b+	b+	ADJ
ajird-807	20	67	+	+	CCONJ
ajird-807	20	68	the	the	DET
ajird-807	20	69	expression	expression	NOUN
ajird-807	20	70	must	must	AUX
ajird-807	20	71	take	take	VERB
ajird-807	20	72	the	the	DET
ajird-807	20	73	smallest	small	ADJ
ajird-807	20	74	value	value	NOUN
ajird-807	20	75	.	.	PUNCT
ajird-807	21	1	so	so	ADV
ajird-807	21	2	,	,	PUNCT
ajird-807	21	3	we	we	PRON
ajird-807	21	4	got	get	VERB
ajird-807	21	5	the	the	DET
ajird-807	21	6	following	follow	VERB
ajird-807	21	7	system	system	NOUN
ajird-807	21	8	:	:	PUNCT
ajird-807	21	9	american	american	PROPN
ajird-807	21	10	journal	journal	PROPN
ajird-807	21	11	of	of	ADP
ajird-807	21	12	interdisciplinary	interdisciplinary	ADJ
ajird-807	21	13	research	research	NOUN
ajird-807	21	14	and	and	CCONJ
ajird-807	21	15	development	development	NOUN
ajird-807	21	16	issn	issn	PROPN
ajird-807	21	17	online	online	NOUN
ajird-807	21	18	:	:	PUNCT
ajird-807	21	19	2771	2771	NUM
ajird-807	21	20	-	-	SYM
ajird-807	21	21	8948	8948	NUM
ajird-807	21	22	website	website	NOUN
ajird-807	21	23	:	:	PUNCT
ajird-807	21	24	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-807	21	25	volume	volume	NOUN
ajird-807	21	26	21	21	NUM
ajird-807	21	27	,	,	PUNCT
ajird-807	21	28	october	october	PROPN
ajird-807	21	29	,	,	PUNCT
ajird-807	21	30	2023	2023	NUM
ajird-807	21	31	153	153	NUM
ajird-807	22	1	|	|	ADV
ajird-807	22	2	p	p	NOUN
ajird-807	22	3	a	a	DET
ajird-807	22	4	g	g	PROPN
ajird-807	22	5	e	e	PROPN
ajird-807	22	6	cos	cos	PROPN
ajird-807	22	7	(	(	PUNCT
ajird-807	22	8	)	)	PUNCT
ajird-807	22	9	1	1	NUM
ajird-807	22	10	1	1	NUM
ajird-807	22	11	cos	cos	PROPN
ajird-807	22	12	(	(	PUNCT
ajird-807	22	13	)	)	PUNCT
ajird-807	22	14	cos	cos	PROPN
ajird-807	22	15	(	(	PUNCT
ajird-807	22	16	)	)	PUNCT
ajird-807	22	17	0	0	NUM
ajird-807	22	18	2	2	NUM
ajird-807	22	19	a	a	DET
ajird-807	22	20	b	b	NOUN
ajird-807	22	21	a	a	DET
ajird-807	22	22	b	b	NOUN
ajird-807	22	23	a	a	DET
ajird-807	22	24	b	b	NOUN
ajird-807	22	25	ìï	ìï	ADP
ajird-807	22	26	=	=	NOUN
ajird-807	22	27	ïï	ïï	ADP
ajird-807	22	28	í	í	NOUN
ajird-807	22	29	ï	ï	NOUN
ajird-807	22	30	+	+	X
ajird-807	23	1	+	+	CCONJ
ajird-807	23	2	=	=	ADJ
ajird-807	23	3	ïïî	ïïî	NOUN
ajird-807	23	4	yoki	yoki	PROPN
ajird-807	23	5	cos	cos	PROPN
ajird-807	23	6	(	(	PUNCT
ajird-807	23	7	)	)	PUNCT
ajird-807	23	8	1	1	NUM
ajird-807	23	9	1	1	NUM
ajird-807	23	10	cos	cos	PROPN
ajird-807	23	11	(	(	PUNCT
ajird-807	23	12	)	)	PUNCT
ajird-807	23	13	.	.	PUNCT
ajird-807	24	1	2	2	NUM
ajird-807	24	2	a	a	DET
ajird-807	24	3	b	b	NOUN
ajird-807	24	4	a	a	DET
ajird-807	24	5	b	b	NOUN
ajird-807	24	6	ìï	ìï	ADP
ajird-807	24	7	=	=	NOUN
ajird-807	24	8	ïï	ïï	ADP
ajird-807	24	9	í	í	PROPN
ajird-807	24	10	ï	ï	NOUN
ajird-807	24	11	+	+	X
ajird-807	24	12	=	=	X
ajird-807	24	13	-ïïî	-ïïî	PUNCT
ajird-807	24	14	from	from	ADP
ajird-807	24	15	this	this	DET
ajird-807	24	16	0a	0a	PROPN
ajird-807	24	17	b=	b=	NOUN
ajird-807	24	18	,	,	PUNCT
ajird-807	24	19	120a	120a	NOUN
ajird-807	24	20	b+	b+	ADV
ajird-807	24	21	=	=	SYM
ajird-807	24	22	o	o	X
ajird-807	24	23	yoki	yoki	PROPN
ajird-807	24	24	a	a	DET
ajird-807	24	25	b=	b=	NOUN
ajird-807	24	26	,	,	PUNCT
ajird-807	24	27	120a	120a	NOUN
ajird-807	24	28	b+	b+	ADP
ajird-807	24	29	=	=	SYM
ajird-807	24	30	o	o	X
ajird-807	24	31	.	.	PUNCT
ajird-807	25	1	finally	finally	ADV
ajird-807	25	2	,	,	PUNCT
ajird-807	25	3	60a	60a	NOUN
ajird-807	25	4	b=	b=	NOUN
ajird-807	26	1	=	=	SYM
ajird-807	27	1	o	o	NOUN
ajird-807	28	1	we	we	PRON
ajird-807	28	2	find	find	VERB
ajird-807	28	3	that	that	SCONJ
ajird-807	28	4	so	so	ADV
ajird-807	28	5	,	,	PUNCT
ajird-807	28	6	the	the	DET
ajird-807	28	7	triangle	triangle	NOUN
ajird-807	28	8	you	you	PRON
ajird-807	28	9	are	be	AUX
ajird-807	28	10	looking	look	VERB
ajird-807	28	11	for	for	ADP
ajird-807	28	12	is	be	AUX
ajird-807	28	13	a	a	DET
ajird-807	28	14	regular	regular	ADJ
ajird-807	28	15	triangle	triangle	NOUN
ajird-807	28	16	.	.	PUNCT
ajird-807	29	1	issue	issue	NOUN
ajird-807	29	2	2	2	NUM
ajird-807	29	3	.	.	PUNCT
ajird-807	30	1	a	a	DET
ajird-807	30	2	dot	dot	NOUN
ajird-807	30	3	is	be	AUX
ajird-807	30	4	given	give	VERB
ajird-807	30	5	in	in	ADP
ajird-807	30	6	a	a	DET
ajird-807	30	7	circle	circle	NOUN
ajird-807	30	8	.	.	PUNCT
ajird-807	31	1	find	find	VERB
ajird-807	31	2	the	the	DET
ajird-807	31	3	smallest	small	ADJ
ajird-807	31	4	distance	distance	NOUN
ajird-807	31	5	passed	pass	VERB
ajird-807	31	6	through	through	ADP
ajird-807	31	7	this	this	DET
ajird-807	31	8	point	point	NOUN
ajird-807	31	9	.	.	PUNCT
ajird-807	32	1	solution	solution	NOUN
ajird-807	32	2	:	:	PUNCT
ajird-807	32	3	given	give	VERB
ajird-807	32	4	r	r	NOUN
ajird-807	32	5	we	we	PRON
ajird-807	32	6	pass	pass	VERB
ajird-807	32	7	two	two	NUM
ajird-807	32	8	wires	wire	NOUN
ajird-807	32	9	through	through	ADP
ajird-807	32	10	the	the	DET
ajird-807	32	11	point	point	NOUN
ajird-807	32	12	.	.	PUNCT
ajird-807	33	1	these	these	DET
ajird-807	33	2	vatars	vatar	NOUN
ajird-807	33	3	ab	ab	PROPN
ajird-807	33	4	and	and	CCONJ
ajird-807	33	5	1	1	NUM
ajird-807	33	6	1	1	NUM
ajird-807	33	7	a	a	DET
ajird-807	33	8	b	b	NOUN
ajird-807	33	9	through	through	ADP
ajird-807	33	10	ab	ab	PROPN
ajird-807	33	11	let	let	VERB
ajird-807	33	12	it	it	PRON
ajird-807	33	13	be	be	AUX
ajird-807	33	14	perpendicular	perpendicular	ADJ
ajird-807	33	15	to	to	ADP
ajird-807	33	16	the	the	DET
ajird-807	33	17	diameter	diameter	NOUN
ajird-807	33	18	of	of	ADP
ajird-807	33	19	the	the	DET
ajird-807	33	20	shaft	shaft	NOUN
ajird-807	33	21	.	.	PUNCT
ajird-807	34	1	1	1	NUM
ajird-807	34	2	1	1	NUM
ajird-807	34	3	a	a	DET
ajird-807	34	4	b	b	NOUN
ajird-807	34	5	let	let	VERB
ajird-807	34	6	it	it	PRON
ajird-807	34	7	be	be	AUX
ajird-807	34	8	voluntary	voluntary	ADJ
ajird-807	34	9	.	.	PUNCT
ajird-807	35	1	1	1	NUM
ajird-807	35	2	1	1	NUM
ajird-807	35	3	a	a	DET
ajird-807	35	4	b	b	NOUN
ajird-807	35	5	home	home	NOUN
ajird-807	35	6	1	1	NUM
ajird-807	35	7	or	or	CCONJ
ajird-807	35	8	we	we	PRON
ajird-807	35	9	pass	pass	VERB
ajird-807	35	10	perpendicularly	perpendicularly	ADV
ajird-807	35	11	and	and	CCONJ
ajird-807	35	12	1	1	NUM
ajird-807	35	13	or	or	CCONJ
ajird-807	35	14	r	r	NOUN
ajird-807	35	15	we	we	PRON
ajird-807	35	16	make	make	VERB
ajird-807	35	17	a	a	DET
ajird-807	35	18	right	right	ADJ
ajird-807	35	19	triangle	triangle	NOUN
ajird-807	35	20	.	.	PUNCT
ajird-807	36	1	in	in	ADP
ajird-807	36	2	this	this	DET
ajird-807	36	3	triangle	triangle	NOUN
ajird-807	36	4	or	or	CCONJ
ajird-807	36	5	gipotenuza	gipotenuza	NOUN
ajird-807	36	6	1	1	NUM
ajird-807	36	7	or	or	CCONJ
ajird-807	36	8	is	be	AUX
ajird-807	36	9	greater	great	ADJ
ajird-807	36	10	than	than	ADP
ajird-807	36	11	the	the	DET
ajird-807	36	12	cathet	cathet	NOUN
ajird-807	36	13	,	,	PUNCT
ajird-807	36	14	so	so	ADV
ajird-807	36	15	,	,	PUNCT
ajird-807	36	16	ab	ab	PROPN
ajird-807	36	17	watar	watar	PROPN
ajird-807	36	18	1	1	NUM
ajird-807	36	19	1	1	NUM
ajird-807	36	20	a	a	DET
ajird-807	36	21	b	b	NOUN
ajird-807	36	22	smaller	small	ADJ
ajird-807	36	23	than	than	ADP
ajird-807	36	24	vatar	vatar	NOUN
ajird-807	36	25	.	.	PUNCT
ajird-807	37	1	it	it	PRON
ajird-807	37	2	follows	follow	VERB
ajird-807	37	3	that	that	SCONJ
ajird-807	37	4	the	the	DET
ajird-807	37	5	circle	circle	NOUN
ajird-807	37	6	is	be	AUX
ajird-807	37	7	given	give	VERB
ajird-807	37	8	r	r	NOUN
ajird-807	37	9	the	the	DET
ajird-807	37	10	smallest	small	ADJ
ajird-807	37	11	distance	distance	NOUN
ajird-807	37	12	from	from	ADP
ajird-807	37	13	a	a	DET
ajird-807	37	14	point	point	NOUN
ajird-807	37	15	is	be	AUX
ajird-807	37	16	the	the	DET
ajird-807	37	17	distance	distance	NOUN
ajird-807	37	18	from	from	ADP
ajird-807	37	19	this	this	DET
ajird-807	37	20	point	point	NOUN
ajird-807	37	21	perpendicular	perpendicular	NOUN
ajird-807	37	22	to	to	ADP
ajird-807	37	23	the	the	DET
ajird-807	37	24	diameter	diameter	NOUN
ajird-807	37	25	.	.	PUNCT
ajird-807	38	1	issue	issue	NOUN
ajird-807	38	2	3	3	NUM
ajird-807	38	3	.	.	NUM
ajird-807	38	4	2r	2r	NOUN
ajird-807	39	1	a	a	DET
ajird-807	39	2	circle	circle	NOUN
ajird-807	39	3	is	be	AUX
ajird-807	39	4	inscribed	inscribe	VERB
ajird-807	39	5	in	in	ADP
ajird-807	39	6	a	a	DET
ajird-807	39	7	triangle	triangle	NOUN
ajird-807	39	8	with	with	ADP
ajird-807	39	9	constant	constant	ADJ
ajird-807	39	10	perimeter	perimeter	NOUN
ajird-807	39	11	.	.	PUNCT
ajird-807	40	1	an	an	DET
ajird-807	40	2	attempt	attempt	NOUN
ajird-807	40	3	was	be	AUX
ajird-807	40	4	made	make	VERB
ajird-807	40	5	to	to	PART
ajird-807	40	6	parallel	parallel	VERB
ajird-807	40	7	the	the	DET
ajird-807	40	8	side	side	NOUN
ajird-807	40	9	of	of	ADP
ajird-807	40	10	the	the	DET
ajird-807	40	11	triangle	triangle	NOUN
ajird-807	40	12	to	to	ADP
ajird-807	40	13	this	this	DET
ajird-807	40	14	circle	circle	NOUN
ajird-807	40	15	.	.	PUNCT
ajird-807	41	1	find	find	VERB
ajird-807	41	2	the	the	DET
ajird-807	41	3	smallest	small	ADJ
ajird-807	41	4	possible	possible	ADJ
ajird-807	41	5	value	value	NOUN
ajird-807	41	6	of	of	ADP
ajird-807	41	7	the	the	DET
ajird-807	41	8	crosssection	crosssection	NOUN
ajird-807	41	9	between	between	ADP
ajird-807	41	10	the	the	DET
ajird-807	41	11	sides	side	NOUN
ajird-807	41	12	of	of	ADP
ajird-807	41	13	this	this	DET
ajird-807	41	14	triangle	triangle	NOUN
ajird-807	41	15	.	.	PUNCT
ajird-807	42	1	solution	solution	NOUN
ajird-807	42	2	:	:	PUNCT
ajird-807	42	3	abc	abc	PROPN
ajird-807	42	4	–	–	PUNCT
ajird-807	42	5	given	give	VERB
ajird-807	42	6	triangle	triangle	NOUN
ajird-807	42	7	.	.	PUNCT
ajird-807	43	1	this	this	PRON
ajird-807	43	2	is	be	AUX
ajird-807	43	3	the	the	DET
ajird-807	43	4	circle	circle	NOUN
ajird-807	43	5	drawn	draw	VERB
ajird-807	43	6	inside	inside	ADP
ajird-807	43	7	the	the	DET
ajird-807	43	8	triangle	triangle	NOUN
ajird-807	43	9	according	accord	VERB
ajird-807	43	10	to	to	ADP
ajird-807	43	11	the	the	DET
ajird-807	43	12	sides	side	NOUN
ajird-807	43	13	,	,	PUNCT
ajird-807	43	14	,	,	PUNCT
ajird-807	43	15	e	e	PROPN
ajird-807	43	16	f	f	PROPN
ajird-807	43	17	d	d	AUX
ajird-807	43	18	try	try	VERB
ajird-807	43	19	at	at	ADP
ajird-807	43	20	the	the	DET
ajird-807	43	21	points.mn	points.mn	NOUN
ajird-807	43	22	the	the	DET
ajird-807	43	23	attempt	attempt	NOUN
ajird-807	43	24	is	be	AUX
ajird-807	43	25	common	common	ADJ
ajird-807	43	26	with	with	ADP
ajird-807	43	27	the	the	DET
ajird-807	43	28	circle	circle	NOUN
ajird-807	43	29	k	k	PROPN
ajird-807	43	30	has	have	VERB
ajird-807	43	31	a	a	DET
ajird-807	43	32	point	point	NOUN
ajird-807	43	33	.	.	PUNCT
ajird-807	44	1	,	,	PUNCT
ajird-807	44	2	mk	mk	VERB
ajird-807	44	3	me	i	PRON
ajird-807	44	4	nf	nf	PROPN
ajird-807	44	5	nk=	nk=	NOUN
ajird-807	44	6	=	=	PRON
ajird-807	44	7	will	will	AUX
ajird-807	44	8	be	be	AUX
ajird-807	44	9	.	.	PUNCT
ajird-807	45	1	so	so	ADV
ajird-807	45	2	,	,	PUNCT
ajird-807	45	3	mn	mn	PROPN
ajird-807	45	4	me	i	PRON
ajird-807	46	1	nf=	nf=	ADV
ajird-807	46	2	+	+	X
ajird-807	46	3	.	.	PUNCT
ajird-807	47	1	likewise	likewise	ADV
ajird-807	47	2	ac	ac	PROPN
ajird-807	47	3	ae	ae	PROPN
ajird-807	47	4	cf=	cf=	PROPN
ajird-807	47	5	+	+	X
ajird-807	47	6	.	.	PUNCT
ajird-807	48	1	based	base	VERB
ajird-807	48	2	on	on	ADP
ajird-807	48	3	these	these	DET
ajird-807	48	4	mbn	mbn	NOUN
ajird-807	48	5	the	the	DET
ajird-807	48	6	perimeter	perimeter	NOUN
ajird-807	48	7	of	of	ADP
ajird-807	48	8	the	the	DET
ajird-807	48	9	triangle	triangle	NOUN
ajird-807	48	10	2	2	NUM
ajird-807	48	11	2p	2p	NUM
ajird-807	48	12	ac	ac	PROPN
ajird-807	48	13	is	be	AUX
ajird-807	48	14	equal	equal	ADJ
ajird-807	48	15	to	to	ADP
ajird-807	48	16	.	.	PUNCT
ajird-807	49	1	mbn	mbn	PROPN
ajird-807	49	2	and	and	CCONJ
ajird-807	49	3	abc	abc	PROPN
ajird-807	49	4	because	because	SCONJ
ajird-807	49	5	the	the	DET
ajird-807	49	6	triangles	triangle	NOUN
ajird-807	49	7	are	be	AUX
ajird-807	49	8	similar	similar	ADJ
ajird-807	49	9	mn	mn	PROPN
ajird-807	49	10	p	p	PROPN
ajird-807	49	11	ac	ac	PROPN
ajird-807	50	1	ac	ac	PROPN
ajird-807	50	2	p	p	PROPN
ajird-807	51	1	=	=	PROPN
ajird-807	51	2	.	.	PUNCT
ajird-807	52	1	mn	mn	PROPN
ajird-807	52	2	y=	y=	PRON
ajird-807	52	3	,	,	PUNCT
ajird-807	52	4	ac	ac	PROPN
ajird-807	52	5	x=	x=	PROPN
ajird-807	53	1	we	we	PRON
ajird-807	53	2	enter	enter	VERB
ajird-807	53	3	the	the	DET
ajird-807	53	4	designations	designation	NOUN
ajird-807	53	5	.	.	PUNCT
ajird-807	54	1	based	base	VERB
ajird-807	54	2	on	on	ADP
ajird-807	54	3	these	these	DET
ajird-807	54	4	y	y	PROPN
ajird-807	54	5	p	p	NOUN
ajird-807	54	6	x	x	X
ajird-807	54	7	x	x	X
ajird-807	54	8	p	p	NOUN
ajird-807	54	9	=	=	X
ajird-807	54	10	.	.	PUNCT
ajird-807	55	1	we	we	PRON
ajird-807	55	2	solve	solve	VERB
ajird-807	55	3	this	this	DET
ajird-807	55	4	equation	equation	NOUN
ajird-807	55	5	with	with	ADP
ajird-807	55	6	respect	respect	NOUN
ajird-807	55	7	to	to	ADP
ajird-807	55	8	u	u	NOUN
ajird-807	55	9	and	and	CCONJ
ajird-807	55	10	1	1	NUM
ajird-807	55	11	(	(	PUNCT
ajird-807	55	12	)	)	PUNCT
ajird-807	55	13	y	y	NOUN
ajird-807	55	14	x	x	PUNCT
ajird-807	55	15	p	p	X
ajird-807	55	16	x	x	X
ajird-807	55	17	p	p	X
ajird-807	55	18	=	=	X
ajird-807	55	19	we	we	PRON
ajird-807	55	20	will	will	AUX
ajird-807	55	21	have	have	VERB
ajird-807	55	22	.	.	PUNCT
ajird-807	56	1	1	1	NUM
ajird-807	56	2	p	p	NOUN
ajird-807	56	3	because	because	SCONJ
ajird-807	56	4	it	it	PRON
ajird-807	56	5	is	be	AUX
ajird-807	56	6	a	a	DET
ajird-807	56	7	constant	constant	ADJ
ajird-807	56	8	quantity	quantity	NOUN
ajird-807	56	9	,	,	PUNCT
ajird-807	56	10	u	u	NOUN
ajird-807	56	11	variable	variable	NOUN
ajird-807	56	12	(	(	PUNCT
ajird-807	56	13	)	)	PUNCT
ajird-807	56	14	x	x	SYM
ajird-807	57	1	p	p	NOUN
ajird-807	57	2	x	x	NOUN
ajird-807	57	3	takes	take	VERB
ajird-807	57	4	the	the	DET
ajird-807	57	5	largest	large	ADJ
ajird-807	57	6	value	value	NOUN
ajird-807	57	7	at	at	ADP
ajird-807	57	8	the	the	DET
ajird-807	57	9	same	same	ADJ
ajird-807	57	10	time	time	NOUN
ajird-807	57	11	as	as	ADP
ajird-807	57	12	multiplication	multiplication	NOUN
ajird-807	57	13	.	.	PUNCT
ajird-807	58	1	(	(	PUNCT
ajird-807	58	2	)	)	PUNCT
ajird-807	58	3	x	x	SYM
ajird-807	58	4	p	p	X
ajird-807	58	5	x	x	X
ajird-807	58	6	and	and	CCONJ
ajird-807	58	7	multiplication	multiplication	NOUN
ajird-807	58	8	(	(	PUNCT
ajird-807	58	9	)	)	PUNCT
ajird-807	58	10	x	x	PROPN
ajird-807	58	11	p	p	X
ajird-807	58	12	x=	x=	PROPN
ajird-807	58	13	,	,	PUNCT
ajird-807	58	14	ya’ni	ya’ni	PROPN
ajird-807	58	15	2	2	NUM
ajird-807	58	16	p	p	NOUN
ajird-807	58	17	x	x	NOUN
ajird-807	58	18	=	=	PRON
ajird-807	58	19	takes	take	VERB
ajird-807	58	20	the	the	DET
ajird-807	58	21	largest	large	ADJ
ajird-807	58	22	value	value	NOUN
ajird-807	58	23	when	when	SCONJ
ajird-807	58	24	so	so	ADV
ajird-807	58	25	,	,	PUNCT
ajird-807	58	26	the	the	DET
ajird-807	58	27	attempted	attempt	VERB
ajird-807	58	28	cross	cross	NOUN
ajird-807	58	29	-	-	NOUN
ajird-807	58	30	section	section	NOUN
ajird-807	58	31	we	we	PRON
ajird-807	58	32	are	be	AUX
ajird-807	58	33	looking	look	VERB
ajird-807	58	34	for	for	ADP
ajird-807	58	35	takes	take	VERB
ajird-807	58	36	the	the	DET
ajird-807	58	37	largest	large	ADJ
ajird-807	58	38	value	value	NOUN
ajird-807	58	39	in	in	ADP
ajird-807	58	40	triangles	triangle	NOUN
ajird-807	58	41	whose	whose	DET
ajird-807	58	42	base	base	NOUN
ajird-807	58	43	is	be	AUX
ajird-807	58	44	equal	equal	ADJ
ajird-807	58	45	to	to	ADP
ajird-807	58	46	a	a	DET
ajird-807	58	47	quarter	quarter	NOUN
ajird-807	58	48	of	of	ADP
ajird-807	58	49	the	the	DET
ajird-807	58	50	perimeter	perimeter	NOUN
ajird-807	58	51	.	.	PUNCT
ajird-807	59	1	there	there	PRON
ajird-807	59	2	are	be	VERB
ajird-807	59	3	an	an	DET
ajird-807	59	4	infinite	infinite	ADJ
ajird-807	59	5	number	number	NOUN
ajird-807	59	6	of	of	ADP
ajird-807	59	7	such	such	ADJ
ajird-807	59	8	triangles	triangle	NOUN
ajird-807	59	9	.	.	PUNCT
ajird-807	60	1	u	u	NOUN
ajird-807	60	2	we	we	PRON
ajird-807	60	3	find	find	VERB
ajird-807	60	4	the	the	DET
ajird-807	60	5	largest	large	ADJ
ajird-807	60	6	value	value	NOUN
ajird-807	60	7	of	of	ADP
ajird-807	60	8	the	the	DET
ajird-807	60	9	variable	variable	ADJ
ajird-807	60	10	max	max	PROPN
ajird-807	60	11	1	1	NUM
ajird-807	60	12	(	(	PUNCT
ajird-807	60	13	)	)	PUNCT
ajird-807	60	14	2	2	NUM
ajird-807	60	15	2	2	NUM
ajird-807	60	16	4	4	NUM
ajird-807	60	17	p	p	NOUN
ajird-807	60	18	p	p	X
ajird-807	60	19	p	p	X
ajird-807	60	20	y	y	PROPN
ajird-807	60	21	p	p	NOUN
ajird-807	60	22	p	p	PROPN
ajird-807	60	23	=	=	X
ajird-807	60	24	×	×	PROPN
ajird-807	60	25	=	=	X
ajird-807	60	26	.	.	PUNCT
ajird-807	61	1	from	from	ADP
ajird-807	61	2	this	this	PRON
ajird-807	61	3	,	,	PUNCT
ajird-807	61	4	it	it	PRON
ajird-807	61	5	follows	follow	VERB
ajird-807	61	6	that	that	SCONJ
ajird-807	61	7	the	the	DET
ajird-807	61	8	intersection	intersection	NOUN
ajird-807	61	9	that	that	PRON
ajird-807	61	10	is	be	AUX
ajird-807	61	11	sought	seek	VERB
ajird-807	61	12	in	in	ADP
ajird-807	61	13	the	the	DET
ajird-807	61	14	triangles	triangle	NOUN
ajird-807	61	15	in	in	ADP
ajird-807	61	16	the	the	DET
ajird-807	61	17	problem	problem	NOUN
ajird-807	61	18	condition	condition	NOUN
ajird-807	61	19	is	be	AUX
ajird-807	61	20	the	the	DET
ajird-807	61	21	middle	middle	ADJ
ajird-807	61	22	line	line	NOUN
ajird-807	61	23	.	.	PUNCT
ajird-807	62	1	american	american	ADJ
ajird-807	62	2	journal	journal	PROPN
ajird-807	62	3	of	of	ADP
ajird-807	62	4	interdisciplinary	interdisciplinary	ADJ
ajird-807	62	5	research	research	NOUN
ajird-807	62	6	and	and	CCONJ
ajird-807	62	7	development	development	NOUN
ajird-807	62	8	issn	issn	PROPN
ajird-807	62	9	online	online	NOUN
ajird-807	62	10	:	:	PUNCT
ajird-807	62	11	2771	2771	NUM
ajird-807	62	12	-	-	SYM
ajird-807	62	13	8948	8948	NUM
ajird-807	62	14	website	website	NOUN
ajird-807	62	15	:	:	PUNCT
ajird-807	62	16	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-807	62	17	volume	volume	NOUN
ajird-807	62	18	21	21	NUM
ajird-807	62	19	,	,	PUNCT
ajird-807	62	20	october	october	PROPN
ajird-807	62	21	,	,	PUNCT
ajird-807	62	22	2023	2023	NUM
ajird-807	62	23	154	154	NUM
ajird-807	62	24	|	|	ADV
ajird-807	62	25	p	p	NOUN
ajird-807	62	26	a	a	DET
ajird-807	62	27	g	g	NOUN
ajird-807	62	28	e	e	NOUN
ajird-807	62	29	issue	issue	NOUN
ajird-807	62	30	4	4	NUM
ajird-807	62	31	.	.	PUNCT
ajird-807	63	1	in	in	ADP
ajird-807	63	2	a	a	DET
ajird-807	63	3	given	give	VERB
ajird-807	63	4	circle	circle	NOUN
ajird-807	63	5	,	,	PUNCT
ajird-807	63	6	a	a	DET
ajird-807	63	7	circle	circle	NOUN
ajird-807	63	8	is	be	AUX
ajird-807	63	9	drawn	draw	VERB
ajird-807	63	10	in	in	ADP
ajird-807	63	11	such	such	DET
ajird-807	63	12	a	a	DET
ajird-807	63	13	way	way	NOUN
ajird-807	63	14	that	that	PRON
ajird-807	63	15	the	the	DET
ajird-807	63	16	sum	sum	NOUN
ajird-807	63	17	of	of	ADP
ajird-807	63	18	the	the	DET
ajird-807	63	19	length	length	NOUN
ajird-807	63	20	of	of	ADP
ajird-807	63	21	the	the	DET
ajird-807	63	22	circle	circle	NOUN
ajird-807	63	23	and	and	CCONJ
ajird-807	63	24	the	the	DET
ajird-807	63	25	length	length	NOUN
ajird-807	63	26	of	of	ADP
ajird-807	63	27	the	the	DET
ajird-807	63	28	distance	distance	NOUN
ajird-807	63	29	from	from	ADP
ajird-807	63	30	the	the	DET
ajird-807	63	31	center	center	NOUN
ajird-807	63	32	of	of	ADP
ajird-807	63	33	the	the	DET
ajird-807	63	34	circle	circle	NOUN
ajird-807	63	35	to	to	ADP
ajird-807	63	36	the	the	DET
ajird-807	63	37	circle	circle	NOUN
ajird-807	63	38	is	be	AUX
ajird-807	63	39	the	the	DET
ajird-807	63	40	largest	large	ADJ
ajird-807	63	41	.	.	PUNCT
ajird-807	64	1	solution	solution	NOUN
ajird-807	64	2	:	:	PUNCT
ajird-807	64	3	method	method	NOUN
ajird-807	64	4	1	1	NUM
ajird-807	64	5	.	.	PUNCT
ajird-807	65	1	looking	look	VERB
ajird-807	65	2	for	for	ADP
ajird-807	65	3	a	a	DET
ajird-807	65	4	home	home	NOUN
ajird-807	65	5	2ab	2ab	NOUN
ajird-807	65	6	a=	a=	NOUN
ajird-807	65	7	,	,	PUNCT
ajird-807	65	8	o	o	INTJ
ajird-807	65	9	–	–	PUNCT
ajird-807	65	10	distance	distance	NOUN
ajird-807	65	11	from	from	ADP
ajird-807	65	12	center	center	NOUN
ajird-807	65	13	to	to	PART
ajird-807	65	14	vatar	vatar	VERB
ajird-807	65	15	od	od	NUM
ajird-807	65	16	d=	d=	NOUN
ajird-807	65	17	let	let	VERB
ajird-807	65	18	it	it	PRON
ajird-807	65	19	be	be	AUX
ajird-807	65	20	2c	2c	NOUN
ajird-807	65	21	a	a	DET
ajird-807	65	22	d=	d=	NOUN
ajird-807	66	1	+	+	CCONJ
ajird-807	66	2	it	it	PRON
ajird-807	66	3	is	be	AUX
ajird-807	66	4	required	require	VERB
ajird-807	66	5	to	to	PART
ajird-807	66	6	find	find	VERB
ajird-807	66	7	the	the	DET
ajird-807	66	8	largest	large	ADJ
ajird-807	66	9	value	value	NOUN
ajird-807	66	10	of	of	ADP
ajird-807	66	11	the	the	DET
ajird-807	66	12	expression	expression	NOUN
ajird-807	66	13	.	.	PUNCT
ajird-807	67	1	the	the	DET
ajird-807	67	2	radius	radius	NOUN
ajird-807	67	3	of	of	ADP
ajird-807	67	4	the	the	DET
ajird-807	67	5	circle	circle	NOUN
ajird-807	67	6	r	r	NOUN
ajird-807	67	7	,	,	PUNCT
ajird-807	67	8	bod	bod	NOUN
ajird-807	67	9	að	að	NOUN
ajird-807	67	10	=	=	NOUN
ajird-807	67	11	let	let	VERB
ajird-807	67	12	it	it	PRON
ajird-807	67	13	be	be	AUX
ajird-807	67	14	.	.	PUNCT
ajird-807	68	1	bdo	bdo	VERB
ajird-807	68	2	from	from	ADP
ajird-807	68	3	a	a	DET
ajird-807	68	4	right	right	ADJ
ajird-807	68	5	triangle	triangle	NOUN
ajird-807	68	6	sin	sin	NOUN
ajird-807	68	7	cos	cos	SCONJ
ajird-807	68	8	a	a	DET
ajird-807	68	9	r	r	NOUN
ajird-807	68	10	d	d	NOUN
ajird-807	68	11	r	r	NOUN
ajird-807	68	12	a	a	DET
ajird-807	68	13	a	a	DET
ajird-807	68	14	ìï	ìï	ADP
ajird-807	68	15	=	=	NOUN
ajird-807	68	16	ï	ï	X
ajird-807	68	17	í	í	NOUN
ajird-807	68	18	ï	ï	NOUN
ajird-807	68	19	=	=	NOUN
ajird-807	68	20	ïî	ïî	NOUN
ajird-807	68	21	we	we	PRON
ajird-807	68	22	find	find	VERB
ajird-807	68	23	.	.	PUNCT
ajird-807	69	1	the	the	DET
ajird-807	69	2	values	value	NOUN
ajird-807	69	3	of	of	ADP
ajird-807	69	4	and	and	CCONJ
ajird-807	69	5	in	in	ADP
ajird-807	69	6	this	this	DET
ajird-807	69	7	system	system	NOUN
ajird-807	69	8	2c	2c	NOUN
ajird-807	69	9	a	a	DET
ajird-807	69	10	d=	d=	NOUN
ajird-807	69	11	+	+	X
ajird-807	69	12	by	by	ADP
ajird-807	69	13	putting	put	VERB
ajird-807	69	14	,	,	PUNCT
ajird-807	69	15	(	(	PUNCT
ajird-807	69	16	2	2	NUM
ajird-807	69	17	sin	sin	NOUN
ajird-807	69	18	cos	cos	NOUN
ajird-807	69	19	)	)	PUNCT
ajird-807	69	20	c	c	PROPN
ajird-807	70	1	r	r	NOUN
ajird-807	70	2	a	a	DET
ajird-807	70	3	a=	a=	NOUN
ajird-807	70	4	+	+	CCONJ
ajird-807	70	5	we	we	PRON
ajird-807	70	6	generate	generate	VERB
ajird-807	70	7	.	.	PUNCT
ajird-807	71	1	if	if	SCONJ
ajird-807	71	2	2	2	NUM
ajird-807	71	3	the	the	DET
ajird-807	71	4	tgj	tgj	NOUN
ajird-807	71	5	if	if	SCONJ
ajird-807	71	6	we	we	PRON
ajird-807	71	7	define	define	VERB
ajird-807	71	8	by	by	ADP
ajird-807	71	9	,	,	PUNCT
ajird-807	71	10	then	then	ADV
ajird-807	71	11	we	we	PRON
ajird-807	71	12	have	have	VERB
ajird-807	71	13	the	the	DET
ajird-807	71	14	following	following	NOUN
ajird-807	71	15	.	.	PUNCT
ajird-807	72	1	(	(	PUNCT
ajird-807	72	2	sin	sin	NOUN
ajird-807	72	3	sin	sin	PROPN
ajird-807	72	4	cos	cos	PROPN
ajird-807	72	5	cos	cos	PROPN
ajird-807	72	6	)	)	PUNCT
ajird-807	72	7	cos	cos	ADP
ajird-807	72	8	r	r	NOUN
ajird-807	72	9	c	c	PROPN
ajird-807	72	10	a	a	DET
ajird-807	72	11	j	j	PROPN
ajird-807	72	12	a	a	DET
ajird-807	72	13	j	j	PROPN
ajird-807	72	14	j	j	PROPN
ajird-807	73	1	=	=	PUNCT
ajird-807	74	1	+	+	CCONJ
ajird-807	74	2	,	,	PUNCT
ajird-807	74	3	or	or	CCONJ
ajird-807	74	4	cos	cos	PROPN
ajird-807	74	5	(	(	PUNCT
ajird-807	74	6	)	)	PUNCT
ajird-807	74	7	cos	cos	ADP
ajird-807	74	8	r	r	NOUN
ajird-807	74	9	c	c	PROPN
ajird-807	74	10	a	a	DET
ajird-807	74	11	j	j	PROPN
ajird-807	74	12	j	j	PROPN
ajird-807	74	13	=	=	PUNCT
ajird-807	74	14	.	.	PUNCT
ajird-807	75	1	c	c	PROPN
ajird-807	75	2	variable	variable	PROPN
ajird-807	75	3	cos	cos	PROPN
ajird-807	75	4	(	(	PUNCT
ajird-807	75	5	)	)	PUNCT
ajird-807	75	6	1a	1a	PROPN
ajird-807	75	7	j=	j=	PROPN
ajird-807	75	8	reaches	reach	VERB
ajird-807	75	9	its	its	PRON
ajird-807	75	10	maximum	maximum	NOUN
ajird-807	75	11	when	when	SCONJ
ajird-807	75	12	0a	0a	PROPN
ajird-807	75	13	j	j	PROPN
ajird-807	75	14	a	a	DET
ajird-807	75	15	j=	j=	NOUN
ajird-807	75	16	þ	þ	PROPN
ajird-807	75	17	=	=	SYM
ajird-807	75	18	da	da	PROPN
ajird-807	75	19	.	.	PUNCT
ajird-807	76	1	2tgj	2tgj	NOUN
ajird-807	76	2	=	=	PUNCT
ajird-807	77	1	because	because	SCONJ
ajird-807	77	2	1	1	NUM
ajird-807	77	3	cos	cos	PROPN
ajird-807	77	4	cos	cos	PROPN
ajird-807	77	5	5	5	NUM
ajird-807	77	6	a	a	DET
ajird-807	77	7	j=	j=	NOUN
ajird-807	77	8	=	=	PUNCT
ajird-807	77	9	.	.	PUNCT
ajird-807	78	1	and	and	CCONJ
ajird-807	78	2	so	so	ADV
ajird-807	78	3	,	,	PUNCT
ajird-807	78	4	max	max	PROPN
ajird-807	78	5	1	1	NUM
ajird-807	78	6	5	5	NUM
ajird-807	78	7	1	1	NUM
ajird-807	78	8	5	5	NUM
ajird-807	78	9	r	r	NOUN
ajird-807	78	10	c	c	NOUN
ajird-807	78	11	r=	r=	ADJ
ajird-807	78	12	×	×	NOUN
ajird-807	78	13	=	=	PUNCT
ajird-807	78	14	is	be	AUX
ajird-807	78	15	the	the	DET
ajird-807	78	16	length	length	NOUN
ajird-807	78	17	of	of	ADP
ajird-807	78	18	the	the	DET
ajird-807	78	19	desired	desire	VERB
ajird-807	78	20	length	length	NOUN
ajird-807	78	21	1	1	NUM
ajird-807	78	22	4	4	NUM
ajird-807	78	23	5	5	NUM
ajird-807	78	24	2	2	NUM
ajird-807	78	25	2	2	NUM
ajird-807	78	26	sin	sin	NOUN
ajird-807	78	27	2	2	NUM
ajird-807	78	28	1	1	NUM
ajird-807	78	29	5	5	NUM
ajird-807	78	30	5	5	NUM
ajird-807	78	31	r	r	NOUN
ajird-807	78	32	a	a	DET
ajird-807	78	33	r	r	NOUN
ajird-807	78	34	ra=	ra=	NOUN
ajird-807	78	35	=	=	PUNCT
ajird-807	79	1	=	=	PUNCT
ajird-807	79	2	is	be	AUX
ajird-807	79	3	equal	equal	ADJ
ajird-807	79	4	to	to	ADP
ajird-807	79	5	.	.	PUNCT
ajird-807	80	1	method	method	PROPN
ajird-807	80	2	2	2	NUM
ajird-807	80	3	.	.	PUNCT
ajird-807	80	4	based	base	VERB
ajird-807	80	5	on	on	ADP
ajird-807	80	6	the	the	DET
ajird-807	80	7	designations	designation	NOUN
ajird-807	80	8	in	in	ADP
ajird-807	80	9	method	method	NOUN
ajird-807	80	10	1	1	NUM
ajird-807	80	11	2	2	NUM
ajird-807	80	12	2d	2d	NOUN
ajird-807	80	13	r	r	NOUN
ajird-807	80	14	a=	a=	NOUN
ajird-807	80	15	,	,	PUNCT
ajird-807	80	16	2d	2d	X
ajird-807	80	17	a	a	DET
ajird-807	80	18	c+	c+	NOUN
ajird-807	80	19	=	=	PUNCT
ajird-807	80	20	from	from	ADP
ajird-807	80	21	2	2	NUM
ajird-807	80	22	22c	22c	NOUN
ajird-807	80	23	a	a	DET
ajird-807	80	24	r	r	NOUN
ajird-807	80	25	a=	a=	NOUN
ajird-807	81	1	+	+	CCONJ
ajird-807	81	2	yoki	yoki	PROPN
ajird-807	81	3	2	2	NUM
ajird-807	81	4	2	2	NUM
ajird-807	81	5	25	25	NUM
ajird-807	81	6	4	4	NUM
ajird-807	81	7	0a	0a	NUM
ajird-807	81	8	ac	ac	PROPN
ajird-807	81	9	c	c	PROPN
ajird-807	81	10	r+	r+	NOUN
ajird-807	81	11	=	=	PRON
ajird-807	81	12	will	will	AUX
ajird-807	81	13	be	be	AUX
ajird-807	81	14	.	.	PUNCT
ajird-807	82	1	this	this	PRON
ajird-807	82	2	is	be	AUX
ajird-807	82	3	when	when	SCONJ
ajird-807	82	4	the	the	DET
ajird-807	82	5	discriminant	discriminant	NOUN
ajird-807	82	6	of	of	ADP
ajird-807	82	7	the	the	DET
ajird-807	82	8	last	last	ADJ
ajird-807	82	9	equation	equation	NOUN
ajird-807	82	10	is	be	AUX
ajird-807	82	11	zero	zero	NUM
ajird-807	82	12	s	s	PART
ajird-807	82	13	reaches	reach	VERB
ajird-807	82	14	a	a	DET
ajird-807	82	15	maximum	maximum	ADJ
ajird-807	82	16	,	,	PUNCT
ajird-807	82	17	i.e	i.e	DET
ajird-807	82	18	2	2	NUM
ajird-807	82	19	2	2	NUM
ajird-807	82	20	24	24	NUM
ajird-807	82	21	5	5	NUM
ajird-807	82	22	5	5	NUM
ajird-807	82	23	0c	0c	NOUN
ajird-807	82	24	c	c	NOUN
ajird-807	82	25	r+	r+	NOUN
ajird-807	82	26	=	=	PUNCT
ajird-807	82	27	at	at	ADP
ajird-807	82	28	from	from	ADP
ajird-807	82	29	this	this	DET
ajird-807	82	30	max	max	PROPN
ajird-807	82	31	5c	5c	NUM
ajird-807	82	32	r=	r=	ADJ
ajird-807	82	33	.	.	PUNCT
ajird-807	83	1	c	c	NOUN
ajird-807	83	2	using	use	VERB
ajird-807	83	3	the	the	DET
ajird-807	83	4	value	value	NOUN
ajird-807	83	5	of	of	ADP
ajird-807	83	6	a	a	PRON
ajird-807	83	7	if	if	SCONJ
ajird-807	83	8	we	we	PRON
ajird-807	83	9	find	find	VERB
ajird-807	83	10	4	4	NUM
ajird-807	83	11	5	5	NUM
ajird-807	83	12	2	2	NUM
ajird-807	83	13	5	5	NUM
ajird-807	83	14	r	r	NOUN
ajird-807	83	15	a	a	NOUN
ajird-807	83	16	=	=	PUNCT
ajird-807	83	17	will	will	AUX
ajird-807	83	18	be	be	AUX
ajird-807	83	19	equal	equal	ADJ
ajird-807	83	20	to	to	PART
ajird-807	83	21	issue	issue	VERB
ajird-807	83	22	5	5	NUM
ajird-807	83	23	.	.	PUNCT
ajird-807	84	1	a	a	DET
ajird-807	84	2	rectangle	rectangle	NOUN
ajird-807	84	3	is	be	AUX
ajird-807	84	4	drawn	draw	VERB
ajird-807	84	5	inside	inside	ADP
ajird-807	84	6	a	a	DET
ajird-807	84	7	semicircle	semicircle	NOUN
ajird-807	84	8	.	.	PUNCT
ajird-807	85	1	two	two	NUM
ajird-807	85	2	ends	end	NOUN
ajird-807	85	3	of	of	ADP
ajird-807	85	4	this	this	DET
ajird-807	85	5	rectangle	rectangle	NOUN
ajird-807	85	6	lie	lie	NOUN
ajird-807	85	7	on	on	ADP
ajird-807	85	8	the	the	DET
ajird-807	85	9	diameter	diameter	NOUN
ajird-807	85	10	,	,	PUNCT
ajird-807	85	11	and	and	CCONJ
ajird-807	85	12	the	the	DET
ajird-807	85	13	other	other	ADJ
ajird-807	85	14	two	two	NUM
ajird-807	85	15	lie	lie	NOUN
ajird-807	85	16	on	on	ADP
ajird-807	85	17	the	the	DET
ajird-807	85	18	semicircle	semicircle	NOUN
ajird-807	85	19	.	.	PUNCT
ajird-807	86	1	a	a	DET
ajird-807	86	2	rectangle	rectangle	NOUN
ajird-807	86	3	with	with	ADP
ajird-807	86	4	the	the	DET
ajird-807	86	5	ratio	ratio	NOUN
ajird-807	86	6	of	of	ADP
ajird-807	86	7	its	its	PRON
ajird-807	86	8	sides	side	NOUN
ajird-807	86	9	will	will	AUX
ajird-807	86	10	have	have	VERB
ajird-807	86	11	the	the	DET
ajird-807	86	12	largest	large	ADJ
ajird-807	86	13	area	area	NOUN
ajird-807	86	14	.	.	PUNCT
ajird-807	87	1	solving	solve	VERB
ajird-807	87	2	:	:	PUNCT
ajird-807	87	3	oc	oc	X
ajird-807	87	4	–	–	PUNCT
ajird-807	87	5	the	the	DET
ajird-807	87	6	radius	radius	NOUN
ajird-807	87	7	of	of	ADP
ajird-807	87	8	the	the	DET
ajird-807	87	9	semicircle	semicircle	NOUN
ajird-807	87	10	,	,	PUNCT
ajird-807	87	11	oca	oca	NOUN
ajird-807	87	12	and	and	CCONJ
ajird-807	87	13	the	the	DET
ajird-807	87	14	acute	acute	PROPN
ajird-807	87	15	angle	angle	NOUN
ajird-807	87	16	between	between	ADP
ajird-807	87	17	the	the	DET
ajird-807	87	18	diameter	diameter	NOUN
ajird-807	87	19	.	.	PUNCT
ajird-807	88	1	cod	cod	NOUN
ajird-807	88	2	from	from	ADP
ajird-807	88	3	a	a	DET
ajird-807	88	4	right	right	ADJ
ajird-807	88	5	triangle	triangle	NOUN
ajird-807	88	6	sin	sin	NOUN
ajird-807	88	7	,	,	PUNCT
ajird-807	88	8	coscd	coscd	NOUN
ajird-807	88	9	oc	oc	PROPN
ajird-807	88	10	od	od	PROPN
ajird-807	88	11	oca	oca	PROPN
ajird-807	88	12	a=	a=	PROPN
ajird-807	89	1	=	=	X
ajird-807	89	2	we	we	PRON
ajird-807	89	3	find	find	VERB
ajird-807	89	4	.	.	PUNCT
ajird-807	90	1	american	american	ADJ
ajird-807	90	2	journal	journal	PROPN
ajird-807	90	3	of	of	ADP
ajird-807	90	4	interdisciplinary	interdisciplinary	ADJ
ajird-807	90	5	research	research	NOUN
ajird-807	90	6	and	and	CCONJ
ajird-807	90	7	development	development	NOUN
ajird-807	90	8	issn	issn	PROPN
ajird-807	90	9	online	online	NOUN
ajird-807	90	10	:	:	PUNCT
ajird-807	90	11	2771	2771	NUM
ajird-807	90	12	-	-	SYM
ajird-807	90	13	8948	8948	NUM
ajird-807	90	14	website	website	NOUN
ajird-807	90	15	:	:	PUNCT
ajird-807	90	16	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-807	90	17	volume	volume	NOUN
ajird-807	90	18	21	21	NUM
ajird-807	90	19	,	,	PUNCT
ajird-807	90	20	october	october	PROPN
ajird-807	90	21	,	,	PUNCT
ajird-807	90	22	2023	2023	NUM
ajird-807	90	23	155	155	NUM
ajird-807	91	1	|	|	ADV
ajird-807	91	2	p	p	NOUN
ajird-807	91	3	a	a	DET
ajird-807	91	4	g	g	PROPN
ajird-807	91	5	e	e	PROPN
ajird-807	91	6	abcd	abcd	PROPN
ajird-807	91	7	rectangular	rectangular	ADJ
ajird-807	91	8	face	face	NOUN
ajird-807	91	9	22	22	NUM
ajird-807	91	10	2	2	NUM
ajird-807	91	11	cos	cos	PROPN
ajird-807	91	12	sin	sin	NOUN
ajird-807	91	13	sin	sin	VERB
ajird-807	91	14	2s	2s	PROPN
ajird-807	91	15	od	od	PROPN
ajird-807	91	16	cd	cd	PROPN
ajird-807	91	17	oc	oc	NOUN
ajird-807	91	18	oc	oc	PROPN
ajird-807	91	19	oca	oca	PROPN
ajird-807	91	20	a	a	DET
ajird-807	91	21	a=	a=	ADJ
ajird-807	91	22	×	×	NOUN
ajird-807	91	23	=	=	SYM
ajird-807	91	24	×	×	NOUN
ajird-807	91	25	=	=	PUNCT
ajird-807	91	26	will	will	AUX
ajird-807	91	27	be	be	AUX
ajird-807	91	28	equal	equal	ADJ
ajird-807	91	29	to	to	ADP
ajird-807	91	30	s	s	PRON
ajird-807	91	31	the	the	DET
ajird-807	91	32	largest	large	ADJ
ajird-807	91	33	value	value	NOUN
ajird-807	91	34	of	of	ADP
ajird-807	91	35	the	the	DET
ajird-807	91	36	surface	surface	NOUN
ajird-807	91	37	sin	sin	NOUN
ajird-807	91	38	2	2	NUM
ajird-807	91	39	1a	1a	NOUN
ajird-807	91	40	=	=	PUNCT
ajird-807	91	41	when	when	SCONJ
ajird-807	91	42	,	,	PUNCT
ajird-807	91	43	1	1	NUM
ajird-807	91	44	c	c	NOUN
ajird-807	91	45	2oc	2oc	NOUN
ajird-807	91	46	will	will	AUX
ajird-807	91	47	be	be	AUX
ajird-807	91	48	equal	equal	ADJ
ajird-807	91	49	to	to	ADP
ajird-807	91	50	,	,	PUNCT
ajird-807	91	51	i.e	i.e	PROPN
ajird-807	91	52	45a	45a	NOUN
ajird-807	91	53	=	=	SYM
ajird-807	92	1	o	o	PROPN
ajird-807	92	2	.	.	PUNCT
ajird-807	93	1	so	so	ADV
ajird-807	93	2	,	,	PUNCT
ajird-807	93	3	2	2	NUM
ajird-807	93	4	ad	ad	NOUN
ajird-807	93	5	cd	cd	NOUN
ajird-807	93	6	=	=	PUNCT
ajird-807	93	7	.	.	PUNCT
ajird-807	94	1	issue	issue	NOUN
ajird-807	94	2	6	6	NUM
ajird-807	94	3	.	.	X
ajird-807	94	4	two	two	NUM
ajird-807	94	5	in	in	ADP
ajird-807	94	6	a	a	DET
ajird-807	94	7	circle	circle	NOUN
ajird-807	94	8	a	a	DET
ajird-807	94	9	and	and	CCONJ
ajird-807	94	10	b	b	NUM
ajird-807	94	11	points	point	NOUN
ajird-807	94	12	are	be	AUX
ajird-807	94	13	given	give	VERB
ajird-807	94	14	.	.	PUNCT
ajird-807	95	1	so	so	ADV
ajird-807	95	2	c	c	PROPN
ajird-807	95	3	find	find	VERB
ajird-807	95	4	the	the	DET
ajird-807	95	5	point	point	NOUN
ajird-807	95	6	such	such	ADJ
ajird-807	95	7	that	that	SCONJ
ajird-807	95	8	the	the	DET
ajird-807	95	9	vatars	vatar	NOUN
ajird-807	95	10	ac	ac	PROPN
ajird-807	95	11	bc×	bc×	PROPN
ajird-807	95	12	let	let	VERB
ajird-807	95	13	the	the	DET
ajird-807	95	14	product	product	NOUN
ajird-807	95	15	be	be	AUX
ajird-807	95	16	the	the	DET
ajird-807	95	17	largest	large	ADJ
ajird-807	95	18	.	.	PUNCT
ajird-807	96	1	solution	solution	NOUN
ajird-807	96	2	:	:	PUNCT
ajird-807	96	3	if	if	SCONJ
ajird-807	96	4	you	you	PRON
ajird-807	96	5	are	be	AUX
ajird-807	96	6	looking	look	VERB
ajird-807	96	7	for	for	ADP
ajird-807	96	8	c	c	PROPN
ajird-807	96	9	points	point	NOUN
ajird-807	96	10	ab	ab	PROPN
ajird-807	96	11	if	if	SCONJ
ajird-807	96	12	we	we	PRON
ajird-807	96	13	take	take	VERB
ajird-807	96	14	it	it	PRON
ajird-807	96	15	on	on	ADP
ajird-807	96	16	one	one	NUM
ajird-807	96	17	side	side	NOUN
ajird-807	96	18	of	of	ADP
ajird-807	96	19	the	the	DET
ajird-807	96	20	watar	watar	NOUN
ajird-807	96	21	,	,	PUNCT
ajird-807	96	22	abc	abc	PROPN
ajird-807	96	23	angle	angle	PROPN
ajird-807	96	24	takes	take	VERB
ajird-807	96	25	the	the	DET
ajird-807	96	26	same	same	ADJ
ajird-807	96	27	values	value	NOUN
ajird-807	96	28	,	,	PUNCT
ajird-807	96	29	this	this	DET
ajird-807	96	30	value	value	NOUN
ajird-807	96	31	a	a	DET
ajird-807	96	32	angle	angle	NOUN
ajird-807	96	33	takes	take	VERB
ajird-807	96	34	the	the	DET
ajird-807	96	35	same	same	ADJ
ajird-807	96	36	values	value	NOUN
ajird-807	96	37	,	,	PUNCT
ajird-807	96	38	this	this	DET
ajird-807	96	39	value	value	NOUN
ajird-807	96	40	1	1	NUM
ajird-807	96	41	c	c	NOUN
ajird-807	96	42	even	even	ADV
ajird-807	96	43	if	if	SCONJ
ajird-807	96	44	the	the	DET
ajird-807	96	45	situation	situation	NOUN
ajird-807	96	46	of	of	ADP
ajird-807	96	47	the	the	DET
ajird-807	96	48	point	point	NOUN
ajird-807	96	49	changes	change	NOUN
ajird-807	96	50	in	in	ADP
ajird-807	96	51	any	any	DET
ajird-807	96	52	way	way	NOUN
ajird-807	96	53	(	(	PUNCT
ajird-807	96	54	ab	ab	NOUN
ajird-807	96	55	on	on	ADP
ajird-807	96	56	one	one	NUM
ajird-807	96	57	side	side	NOUN
ajird-807	96	58	from	from	ADP
ajird-807	96	59	)	)	PUNCT
ajird-807	96	60	1	1	NUM
ajird-807	96	61	sin	sin	NOUN
ajird-807	96	62	2	2	NUM
ajird-807	96	63	ac	ac	NOUN
ajird-807	96	64	bc	bc	PROPN
ajird-807	96	65	a×	a×	PROPN
ajird-807	96	66	×	×	PROPN
ajird-807	96	67	expression	expression	NOUN
ajird-807	96	68	abc	abc	PROPN
ajird-807	96	69	gives	give	VERB
ajird-807	96	70	the	the	DET
ajird-807	96	71	face	face	NOUN
ajird-807	96	72	of	of	ADP
ajird-807	96	73	the	the	DET
ajird-807	96	74	triangle	triangle	NOUN
ajird-807	96	75	.	.	PUNCT
ajird-807	97	1	this	this	PRON
ajird-807	97	2	is	be	AUX
ajird-807	97	3	the	the	DET
ajird-807	97	4	surface	surface	NOUN
ajird-807	97	5	ac	ac	PROPN
ajird-807	97	6	bc×	bc×	PROPN
ajird-807	97	7	from	from	ADP
ajird-807	97	8	magnitude	magnitude	NOUN
ajird-807	97	9	,	,	PUNCT
ajird-807	97	10	a	a	DET
ajird-807	97	11	constant	constant	ADJ
ajird-807	97	12	multiplier	multipli	ADJ
ajird-807	97	13	1	1	NUM
ajird-807	97	14	sin	sin	NOUN
ajird-807	97	15	2	2	NUM
ajird-807	97	16	a	a	DET
ajird-807	97	17	differs	differ	NOUN
ajird-807	97	18	from	from	ADP
ajird-807	97	19	abc	abc	PROPN
ajird-807	97	20	triangular	triangular	PROPN
ajird-807	97	21	face	face	NOUN
ajird-807	97	22	,	,	PUNCT
ajird-807	97	23	ac	ac	PROPN
ajird-807	97	24	bc×	bc×	PROPN
ajird-807	97	25	reaches	reach	VERB
ajird-807	97	26	its	its	PRON
ajird-807	97	27	maximum	maximum	ADJ
ajird-807	97	28	value	value	NOUN
ajird-807	97	29	simultaneously	simultaneously	ADV
ajird-807	97	30	with	with	ADP
ajird-807	97	31	multiplication	multiplication	NOUN
ajird-807	97	32	.	.	PUNCT
ajird-807	98	1	but	but	CCONJ
ajird-807	98	2	ab	ab	PROPN
ajird-807	98	3	ohas	oha	VERB
ajird-807	98	4	an	an	DET
ajird-807	98	5	unchanging	unchanging	ADJ
ajird-807	98	6	basis	basis	NOUN
ajird-807	98	7	abc	abc	NOUN
ajird-807	98	8	the	the	DET
ajird-807	98	9	maximum	maximum	ADJ
ajird-807	98	10	value	value	NOUN
ajird-807	98	11	of	of	ADP
ajird-807	98	12	the	the	DET
ajird-807	98	13	face	face	NOUN
ajird-807	98	14	of	of	ADP
ajird-807	98	15	the	the	DET
ajird-807	98	16	triangle	triangle	NOUN
ajird-807	98	17	is	be	AUX
ajird-807	98	18	at	at	ADP
ajird-807	98	19	the	the	DET
ajird-807	98	20	maximum	maximum	ADJ
ajird-807	98	21	value	value	NOUN
ajird-807	98	22	of	of	ADP
ajird-807	98	23	the	the	DET
ajird-807	98	24	height	height	NOUN
ajird-807	98	25	lowered	lower	VERB
ajird-807	98	26	to	to	ADP
ajird-807	98	27	the	the	DET
ajird-807	98	28	base	base	NOUN
ajird-807	98	29	.	.	PUNCT
ajird-807	99	1	from	from	ADP
ajird-807	99	2	this	this	DET
ajird-807	99	3	1	1	NUM
ajird-807	99	4	c	c	NOUN
ajird-807	99	5	point	point	NOUN
ajird-807	99	6	circle	circle	NOUN
ajird-807	99	7	and	and	CCONJ
ajird-807	99	8	ab	ab	PROPN
ajird-807	99	9	it	it	PRON
ajird-807	99	10	follows	follow	VERB
ajird-807	99	11	that	that	SCONJ
ajird-807	99	12	it	it	PRON
ajird-807	99	13	is	be	AUX
ajird-807	99	14	the	the	DET
ajird-807	99	15	point	point	NOUN
ajird-807	99	16	of	of	ADP
ajird-807	99	17	intersection	intersection	NOUN
ajird-807	99	18	of	of	ADP
ajird-807	99	19	the	the	DET
ajird-807	99	20	middle	middle	ADJ
ajird-807	99	21	perpendicular	perpendicular	NOUN
ajird-807	99	22	of	of	ADP
ajird-807	99	23	the	the	DET
ajird-807	99	24	vatar	vatar	NOUN
ajird-807	99	25	.	.	PUNCT
ajird-807	100	1	this	this	DET
ajird-807	100	2	mid	mid	ADJ
ajird-807	100	3	-	-	ADJ
ajird-807	100	4	perpendicular	perpendicular	ADJ
ajird-807	100	5	intersects	intersect	NOUN
ajird-807	100	6	the	the	DET
ajird-807	100	7	circle	circle	NOUN
ajird-807	100	8	at	at	ADP
ajird-807	100	9	two	two	NUM
ajird-807	100	10	points	point	NOUN
ajird-807	100	11	.	.	PUNCT
ajird-807	101	1	from	from	ADP
ajird-807	101	2	these	these	DET
ajird-807	101	3	points	point	NOUN
ajird-807	101	4	ab	ab	PROPN
ajird-807	101	5	the	the	DET
ajird-807	101	6	one	one	NOUN
ajird-807	101	7	that	that	PRON
ajird-807	101	8	is	be	AUX
ajird-807	101	9	far	far	ADV
ajird-807	101	10	away	away	ADV
ajird-807	101	11	from	from	ADP
ajird-807	101	12	will	will	AUX
ajird-807	101	13	be	be	AUX
ajird-807	101	14	the	the	DET
ajird-807	101	15	sought	seek	VERB
ajird-807	101	16	point	point	NOUN
ajird-807	101	17	.	.	PUNCT
ajird-807	102	1	in	in	ADP
ajird-807	102	2	our	our	PRON
ajird-807	102	3	drawing	drawing	NOUN
ajird-807	102	4	it	it	PRON
ajird-807	102	5	is	be	AUX
ajird-807	102	6	1	1	NUM
ajird-807	102	7	c	c	NOUN
ajird-807	102	8	there	there	PRON
ajird-807	102	9	will	will	AUX
ajird-807	102	10	be	be	AUX
ajird-807	102	11	a	a	DET
ajird-807	102	12	point	point	NOUN
ajird-807	102	13	.	.	PUNCT
ajird-807	103	1	references	reference	NOUN
ajird-807	103	2	1	1	NUM
ajird-807	103	3	.	.	PUNCT
ajird-807	104	1	shklyarskiy	shklyarskiy	PROPN
ajird-807	104	2	d.	d.	PROPN
ajird-807	104	3	o.	o.	PROPN
ajird-807	104	4	,	,	PUNCT
ajird-807	104	5	chensov	chensov	PROPN
ajird-807	104	6	n.	n.	PROPN
ajird-807	104	7	n.	n.	PROPN
ajird-807	104	8	,	,	PUNCT
ajird-807	104	9	yaglom	yaglom	PROPN
ajird-807	104	10	i.	i.	PROPN
ajird-807	104	11	m.	m.	PROPN
ajird-807	104	12	geometricheskie	geometricheskie	PROPN
ajird-807	104	13	neravenstva	neravenstva	NOUN
ajird-807	104	14	i	i	PRON
ajird-807	104	15	zadachi	zadachi	VERB
ajird-807	105	1	na	na	VERB
ajird-807	105	2	maksimum	maksimum	NOUN
ajird-807	106	1	i	i	PRON
ajird-807	106	2	minimum	minimum	NOUN
ajird-807	106	3	.	.	PUNCT
ajird-807	107	1	—	—	PUNCT
ajird-807	107	2	m.	m.	NOUN
ajird-807	107	3	:	:	PUNCT
ajird-807	107	4	nauka	nauka	PROPN
ajird-807	107	5	,	,	PUNCT
ajird-807	107	6	1970	1970	NUM
ajird-807	107	7	.	.	PUNCT
ajird-807	108	1	2	2	NUM
ajird-807	108	2	.	.	X
ajird-807	109	1	b	b	NUM
ajird-807	109	2	o	o	X
ajird-807	109	3	l	l	NOUN
ajird-807	110	1	t	t	NOUN
ajird-807	110	2	ya	ya	PROPN
ajird-807	111	1	n	n	PROPN
ajird-807	111	2	s	s	PART
ajird-807	111	3	k	k	NOUN
ajird-807	112	1	i	i	PRON
ajird-807	112	2	y	y	PROPN
ajird-807	112	3	v.	v.	PROPN
ajird-807	112	4	g.	g.	PROPN
ajird-807	112	5	,	,	PUNCT
ajird-807	112	6	ya	ya	PROPN
ajird-807	112	7	g	g	NOUN
ajird-807	112	8	l	l	NOUN
ajird-807	112	9	o	o	X
ajird-807	112	10	m	m	PROPN
ajird-807	112	11	i.	i.	PROPN
ajird-807	112	12	m.	m.	PROPN
ajird-807	112	13	geometricheskie	geometricheskie	PROPN
ajird-807	112	14	zadachi	zadachi	PROPN
ajird-807	112	15	na	na	INTJ
ajird-807	112	16	maksimum	maksimum	NOUN
ajird-807	113	1	i	i	PRON
ajird-807	113	2	minimum	minimum	PROPN
ajird-807	113	3	//	//	PROPN
ajird-807	113	4	ensiklopediya	ensiklopediya	NOUN
ajird-807	113	5	elementarnoy	elementarnoy	VERB
ajird-807	113	6	matematiki	matematiki	PRON
ajird-807	113	7	.	.	PUNCT
ajird-807	114	1	kn	kn	PROPN
ajird-807	114	2	.	.	PUNCT
ajird-807	114	3	4.—m	4.—m	NUM
ajird-807	114	4	.	.	PUNCT
ajird-807	114	5	:	:	PUNCT
ajird-807	115	1	nauka	nauka	PROPN
ajird-807	115	2	,	,	PUNCT
ajird-807	115	3	1966	1966	NUM
ajird-807	115	4	.	.	PUNCT
ajird-807	116	1	s.	s.	PROPN
ajird-807	116	2	307—348	307—348	PROPN
ajird-807	116	3	.	.	PUNCT
ajird-807	117	1	3	3	X
ajird-807	117	2	.	.	X
ajird-807	117	3	ponarin	ponarin	PROPN
ajird-807	117	4	ya	ya	PROPN
ajird-807	117	5	.	.	PUNCT
ajird-807	118	1	p.	p.	NOUN
ajird-807	118	2	elementarnaya	elementarnaya	PROPN
ajird-807	119	1	geometriya	geometriya	PROPN
ajird-807	119	2	:	:	PUNCT
ajird-807	119	3	v	v	NOUN
ajird-807	119	4	2	2	NUM
ajird-807	119	5	t.—t	t.—t	NUM
ajird-807	119	6	.	.	PUNCT
ajird-807	120	1	1	1	NUM
ajird-807	120	2	:	:	PUNCT
ajird-807	120	3	planimetriya	planimetriya	NOUN
ajird-807	120	4	,	,	PUNCT
ajird-807	120	5	preobrazovaniya	preobrazovaniya	PROPN
ajird-807	120	6	ploskosti	ploskosti	PROPN
ajird-807	120	7	.	.	PUNCT
ajird-807	121	1	—	—	PUNCT
ajird-807	121	2	m.	m.	NOUN
ajird-807	121	3	:	:	PUNCT
ajird-807	121	4	msnmo	msnmo	NOUN
ajird-807	121	5	,	,	PUNCT
ajird-807	121	6	2004	2004	NUM
ajird-807	121	7	.	.	PUNCT
ajird-807	121	8	—	—	PUNCT
ajird-807	122	1	312	312	NUM
ajird-807	122	2	s.	s.	PROPN
ajird-807	122	3	4	4	NUM
ajird-807	122	4	.	.	PUNCT
ajird-807	122	5	saparboev	saparboev	PROPN
ajird-807	122	6	j.	j.	PROPN
ajird-807	122	7	,	,	PUNCT
ajird-807	122	8	egamov	egamov	PROPN
ajird-807	122	9	m.	m.	NOUN
ajird-807	122	10	akademik	akademik	PROPN
ajird-807	122	11	lisey	lisey	PROPN
ajird-807	122	12	o‘quvchilarining	o‘quvchilarining	PROPN
ajird-807	122	13	fazoviy	fazoviy	PROPN
ajird-807	122	14	tasavvurini	tasavvurini	PROPN
ajird-807	122	15	va	va	PROPN
ajird-807	122	16	matematik	matematik	PROPN
ajird-807	122	17	tafakkurini	tafakkurini	NOUN
ajird-807	122	18	rivojlantirishda	rivojlantirishda	NOUN
ajird-807	122	19	ba’zi	ba’zi	NOUN
ajird-807	122	20	masalalar.//tabiiy	masalalar.//tabiiy	PUNCT
ajird-807	122	21	fanlarni	fanlarni	NOUN
ajird-807	122	22	o‘qitishni	o‘qitishni	X
ajird-807	122	23	gumanitarlashtirish	gumanitarlashtirish	PROPN
ajird-807	122	24	.	.	PUNCT
ajird-807	123	1	universitet	universitet	NOUN
ajird-807	123	2	ilmiy	ilmiy	NOUN
ajird-807	123	3	-	-	PUNCT
ajird-807	123	4	amaliy	amaliy	ADV
ajird-807	123	5	konferensiya	konferensiya	PROPN
ajird-807	123	6	materiallari	materiallari	PROPN
ajird-807	123	7	.	.	PUNCT
ajird-807	124	1	2012y	2012y	NOUN
ajird-807	124	2	.	.	PUNCT
ajird-807	125	1	tdpu	tdpu	PROPN
ajird-807	125	2	.	.	PUNCT
ajird-807	126	1	a	a	DET
ajird-807	126	2	b	b	NOUN
ajird-807	126	3	α	α	NOUN
ajird-807	126	4	o	o	X
ajird-807	126	5	d	d	X
ajird-807	126	6	c	c	PROPN
ajird-807	126	7	.	.	PUNCT
ajird-807	127	1	a	a	DET
ajird-807	127	2	c1	c1	PROPN
ajird-807	127	3	c	c	PROPN
ajird-807	127	4	b	b	PROPN