Question

Prove that a cyclic parallelogram is a rectangle.

Answer 1

Given : ABCD is a cyclic parallelogram. 

To prove : ABCD is a rectangle. 

Proof : ∠ABC = ∠ADC ...(i) [Opposite angles of a ||gm are equal] 

But, ∠ABC + ∠ADC = 180° ... (ii) 

[Sum of opposite angles of a cyclic quadrilateral is 180°] 

⇒ ∠ABC = ∠ADC = 90° [From (i) and (ii)] 

∴ ABCD is a rectangle [A ||gm one of whose angles is 90° is a rectangle] 

Hence, a cyclic parallelogram is a rectangle. Proved.