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ABCD is a parallelogram . The circle pas...

ABCD is a parallelogram . The circle passing through the vertices. A, B and C intersects CD (or CD produced) at E. Prove that `AE=AD`.

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`angle1 +angle4 =180^@` (L.P.A.) ......(1)
`angle 2+angle3 =180^@` ........(2)
(sum of opposite of a cyclic quadrilateral is `180^@`)
`therefore` From (1) and (2), we get
`angle1 +angle4 =angle2 +anlge3` ......(3)
But (opposite angles of a parallelogram )
`therefore` From (3) and (4) ,
`angle1 +angle4 =angle2 +angle4`
`rArrangle1 =angle2`
`rArrAE=AD" "(because" sides opposite to equal angles are equal")`
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