Question

Show that any rectangle is a cyclic quadrilateral.​

Answer 1

Answer:

We know, if a pair of opposite angles of a quadrilateral is supplementary, then quadrilateral is cyclic. ∴ Rectangle ABCD is a cyclic quadrilateral. So, any rectangle is a cyclic quadrilateral.

Answer 2

Answer:

Given: ABCD is a rectangle.

To prove: ABCD is a cyclic quadrilateral.

Proof: ⟂XBCD is a rectangle.

[Given] ∴ ∠A = ∠B = ∠C = ∠D = 90° [Angles of a rectangle] Now, ∠A + ∠C = 90° + 90°

∴ ∠A + ∠C = 180° ∴ ⟂ABCD is a cyclic quadrilateral. [Converse of cyclic quadrilateral theorem