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.