Question

In the figure, ABC is a triangle in which AB=AC. Also a circle passing through B and C intersects the sides AB and AC at the points D and E respectively.

PROVE: AD=AE

Answer 1

To prove that DE is parallel to BC,

if we prove that angle ADE = Angle ABC , hence it will be proved because of corresponding angle property

so we will prove it first

In ΔABC,

∠B = ∠C   .... (1)

In the cyclic quadrilateral CBDE, side BD is produced to A.

We know that exterior angle is equal to opposite interior angle.

i.e. ∠ADE = ∠C .... (2)

From (1) and (2) –

∠ADE = ∠ABC

SO corresponding angles are equal

Ans hence  DE is parrallel to BC

Answer 2

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Step-by-step explanation:

To prove that DE is parallel to BC,

if we prove that angle ADE = Angle ABC , hence it will be proved because of corresponding angle property

so we will prove it first

In ΔABC,

∠B = ∠C   .... (1)

In the cyclic quadrilateral CBDE, side BD is produced to A.

We know that exterior angle is equal to opposite interior angle.

i.e. ∠ADE = ∠C .... (2)

From (1) and (2) –

∠ADE = ∠ABC

SO corresponding angles are equal

Ans hence  DE is parrallel to BC