Question

n 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


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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

Note:-

• Required Diagram is in attachment!