Question

Prove that, any rectangle is a cyclic quadrilateral.

Answer 1

Given: ▢ABCD is a rectangle.

To prove: ▢ABCD is a cyclic quadrilateral.

Proof:

▢ABCD is a rectangle.   ...[Given]

∴ ∠A = ∠B = ∠C = ∠D = 90°   ...[Angles of a rectangle]

Now, ∠A + ∠C = 90° + 90° 

∴ ∠A + ∠C = 180°

We know, if a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.

∴ ▢ABCD is a cyclic quadrilateral.   ...[Converse of cyclic quadrilateral theorem]

So, any rectangle is a cyclic quadrilateral.