# 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

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respectively .prove that DE is parallel to side BC

2
by rishilaugh

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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