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# Prove that a cyclic parallelogram is a rectangle.

Given:
PQRS is a parallelogram inscribed in a circle.

To prove: PQRS is a rectangle.

Proof:
Since, PQRS is a cyclic quadrilateral.

Thus, $$\angle{P}$$ + $$\angle{R}$$ = $$180^\circ$$ ...(i)
(Since, Sum of opposite angles in a cyclic quadrilateral is $$180^\circ$$)

But, $$\angle{P}$$ = $$\angle{R}$$ ...(ii)
(Since, in a parallelogram, opposite angles are equal)

from eq. (i) and (ii), we get,

$$\angle{P}$$ = $$\angle{R}$$ = $$90^\circ$$

Similarly,
$$\angle{Q}$$ = $$\angle{S}$$ = $$90^\circ$$

Thus, Each angle of PQRS is $$90^\circ$$.

Hence, it is proved that PQRS is a rectangle.