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

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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]

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