In the above figure $E$ is any point on median $A D$ of $△ A B C$ . $A, B, C$ and $D$ are four points on a circle. $A C$ and $B D$ intersect at a point $E$ such that $∠ B E C = 130^{\circ}$ and $∠ E C D = 20$ .Find $∠ B A C$

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Solution

In $Δ E D C$
$∠ B E C = ∠ E D C + ∠ D C E$ (by external angle)
$130^{o} = ∠ E D C + 20^{o}$
$∠ E D C = 110^{o}$

$∠ B A C = ∠ B D C$ (by common chord. preperation)
$∴ ∠ B A C = 110^{o}$

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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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Question 5
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 $∠ B E C = 130^{\circ}$ and $∠ E C D = 20^{\circ}$ . Find $∠ B A C$ .

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

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In the above figure E is any point on median AD of △ABC. 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

In ΔEDC∠BEC=∠EDC+∠DCE (by external angle)130o=∠EDC+20o∠EDC=110o∠BAC=∠BDC (by common chord. preperation)∴∠BAC=110o

In the above figure $E$ is any point on median $A D$ of $△ A B C$ . $A, B, C$ and $D$ are four points on a circle. $A C$ and $B D$ intersect at a point $E$ such that $∠ B E C = 130^{\circ}$ and $∠ E C D = 20$ .Find $∠ B A C$

In $Δ E D C$
$∠ B E C = ∠ E D C + ∠ D C E$ (by external angle)
$130^{o} = ∠ E D C + 20^{o}$
$∠ E D C = 110^{o}$

$∠ B A C = ∠ B D C$ (by common chord. preperation)
$∴ ∠ B A C = 110^{o}$