# In an isosceles triangle ABC with AB=AC ,a circle passing through b and c INTERSECTS THE SIDES AB AND intersects the sides AB and AC AT D and E respectively .prove that DE is parallel to side BC

2
by rishilaugh

Log in to add a comment

by rishilaugh

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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

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

The Brainliest Answer!