Question

Prove that a cyclic parallelogram is a rectangle.

Answer 1

Let ABCD be a cyclic parallelogram.

∠A = ∠C and ∠B = ∠D

∠A + ∠C = 180° (Opposite angles of a cyclic quadrilateral) ... (1) 

We know that opposite angles of a parallelogram are equal.

From equation (1),

∠A + ∠C = 180°

∠A + ∠A = 180°

∠2∠A = 180°

∠A = 90°

Parallelogram ABCD has one of its interior angles as 90°. Therefore, it is a rectangle.