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Condition for Two Lines to Be Parallel

In Figure, A,...

Question

In Figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $∠ B E C = 130^{o} a n d ∠ E C D = 20^{o}$ . Then $∠ B A C$ is

140^{o} .

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110^{o} .

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70^{o} .

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120^{o} .

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Solution

The correct option is C $110^{o} .$
$G i v e n - A, B, C & D a r e p o i n t s o n t h e c i r c u m f e r e n c e o f a c i r c l e . A C & B D i n t e r s e c t a t E . A B & C D h a v e b e e n j o i n e d . ∠ B E C = 130^{o} & ∠ E C D = 20^{o} . T o f i n d o u t - ∠ B A C = ? S o l u t i o n - W e j o i n B C . ∠ D E C + ∠ B E C = 180^{o} . (l i n e a r p a i r) ∴ ∠ D E C = 180^{o} - ∠ B E C = 180^{o} - 130^{o} = 50^{o} . S o, i n Δ D E C, w e h a v e ∠ C D E = 180^{o} - (∠ D E C + ∠ E C D) = 180^{o} - (50^{o} + 20^{o}) = 110^{o} . (a n g l e s u m p r o p e r t y o f t r i a n g l e s) N o w t h e c h o r d B C s u b t e n d s ∠ C D E & ∠ B A C t o t h e c i r c u m f e r e n c e o f t h e g i v e n c i r c l e a t D & A r e s p e c t i v e l y . ∴ ∠ C D E = ∠ B A C = a n g l e (s i n c e t h e a n g l e s, s u b t e n d e d b y a c h o r d o f a c i r c l e t o d i f f e r e n t p o i n t s o f t h e c i r c u m f e r e c e o f t h e s a m e c i r c l e, a r e e q u a l) . A n s - O p t i o n B .$

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Similar questions

Q. In figure,

A, B, C

and

D

are four points on a circle.

A C

and

B D

intersect at a point

E

such that

∠ B E C = 130^{o}

and

∠ E C D = 20^{o}

. Find

∠ B A C

A, B, C

and

D

are four points on a circle.

A C

and

B D

intersect at a point

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such that

∠ B E C = 130^{o}

and

∠ E C D = 20^{o}

, then

∠ B A C

is __________.

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In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130 and ∠ECD = 20. Find ∠BAC

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In Figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC=130oand∠ECD=20o. Then ∠BAC is

In Figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $∠ B E C = 130^{o} a n d ∠ E C D = 20^{o}$ . Then $∠ B A C$ is