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Question

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

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Solution

From the figure,

ADE+ADC=180o (Linear pair) ....... (i)

Also, ABCE is a cyclic quadrilateral.

So, AED+ABC=180o ....... (ii) (opposite angles of cyclic quadrilateral sum upto 180o)

ADC=ABC ....... (iii) (Opposite angles of a parallellogram are equal)

Using (i), (ii) and (iii),

AED+ABC=ADE+ABC

AED=ADE

Now, In AED,

AED=ADE

AD=DE (Sides opposite to equal angles)


496250_464062_ans.PNG

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