Question

ABCD is a parallelogram. The circle through A, B, C intersects CD (produced if necessary) at E. Prove that AD = AE.

Answer 1

Given : ABCD is a parallelogram. The circle through A, B, C intersects CD, when produced in E.

To prove : AE = AD.

Proof : Since ABCE is a cyclic quadrilateral

∴ ∠1 + ∠2 = 180⁰ ....(i) [opposite angles of a cyclio quadrilateral are supplementary]

Now inΔADE, since ∠1 = ∠4

AD = AE [Sides opp. to equal angles of a triangle are equal]