**Data : **ABCD is a parallelogram.

The circle through A, B and C intersect CD at E. AE is joined.

**To Prove:** AE = AD

**Proof:** ∠AEC + ∠AED = 180° …………. (i) (linear pair)

ABCE is a cyclic quadrilateral.

∴ ∠ABC + ∠AEC = 180° ………….(ii)

(opposite angles) Comparing (i) and (ii),

∠AEC = ∠AED = ∠ABC + ∠AEC

∠AED = ∠ABC ………….. (iii)

But, ∠ABC = ∠ADE (Opposite angles of quadrilateral)

Substituting in equation (iii),

∠AED = ∠ADE

∴ AE = AD.