Question

Prove that a parallelogram inscribed in a circle is a rectangle.

Answer 1

Parallelogram $ABCD$ is cyclic.

$\angle A+\angle C={180}^0$ (opposite angle of cyclic quadrilateral)

But

$\angle A+\angle C={90}^0$ …….(1) (opposite angle of parallelogram are equal)

Similarly,$\angle B+\angle D={180}^0$

But

$\angle B+\angle D={90}^0$ …….(2) (opposite angle of parallelogram are equal)

$AB=CD$ and $AD=BC$ ……(3) (opposite sides of parallelogram)

Opposite sides are equal and each angle is right angle.

Hence, $ABCD$ is a rectangle.