Question

Abcd is a parallelogram . the circle through A, BAND C intersects CD produced atE, prove that AE=AD

Answer 1

ABCE is a cyclic quadrilateral.

ABC + ADC =180 (I)

Also, EDC is a straight line.

ADE + ADC = 180

But, ADC = ABC (opp. angle of a parallelogram)

ADE + ABC = 180 (ii)

This, ABC + AED = ADE + ABC [from(I) and (ii)]

AED = ADE

AD =AE (opp.sides of equal angles of triangle ADE)

Hence, AD = AE

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