# ABCD is a parallelogram. The circle through A, B and C intersect CD (produced ifnecessary) at E. Prove that A E = A D.

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ABCD is a parallelogram. The circle through A, B and C intersect CD (produced ifnecessary) at E. Prove that A E = A D.

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ABCD is a parallelogram
/_ADC=/_ABC
Point E also lies on circle ABCE is a cyclic quadrilateral
/_AEC+/_ABC=180^0
/_AEC=180-/_ADC
/_AED=/_ADC
/AED=/_ADE
In/_ADE
/_AED=/_ADE