Cyclic Quadrilateral: Parallelogram A quadrilateral is called a cyclic quadrilateral if its all vertices lie on a circle. A cyclic quadrilateral has some special properties: The sum of either pair of opposite angles of a cyclic quadrilateral is 180. OR The opposite angle of a cyclic quadrilateral are supplementary.
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Example: ABCD is a parallelogram. The circle through A, B and C intersects CD produced at E prove that AE = AD.
Solution: In order to prove that AE=AD i.e. AED is an isosceles triangle it is sufficient to prove that AED = ADE.

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