Question

Question 12
Prove that a cyclic parallelogram is a rectangle.

Answer 1

Let ABCD be a cyclic parallelogram.
$\angle A+\angle C={180}^{\circ }$ (Opposite angles of a cyclic quadrilateral)
We know that opposite angles of a parallelogram are equal.
$\therefore \angle A=\angle Cand\angle B=\angle D$
$\angle A+\angle C={180}^{\circ }$
Then $\angle A+\angle A={180}^{\circ }$
$\therefore 2\angle A={180}^{\circ }$
$\Rightarrow \angle A=\angle C={90}^{\circ }$
Parallelogram ABCD has one of its interior angles as ${90}^{\circ }$. Therefore, it is a rectangle.