Prove that a parallelogram which is not a rectangle is not cyclic.

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Solution

PQRS is cyclic quadrilateral.
∠P + ∠R = 180
Also in a parallelogram opposite angles will be equal.
∠P + ∠R = 180°
∠P = ∠R = 90°.

This means that PQRS must be a rectangle, otherwise, it is not cyclic.

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