Question

Prove that a cyclic parallelogram is a rectangle.

Answer 1

ABCD is a cyclic parallelogram in the circle with ‘O’ centre. 

To Prove: ABCD is a rectangle. 

Proof: ABCD is a cyclic parallelogram. 

∴ AB || DC and AD || BC 

∠A = ∠C (Opposite angles of parallelogram) 

But, ∠A + ∠C = 180° 

(Opposites angles of cyclic quadrilateral) 

∠A + ∠A = 180° 

2∠A = 180° 

∠A = \(\frac{180}{2}\)

∴ ∠A = 90° 

If each angle of parallelogram is right angle, it is a rectangle. 

∴ ABCD is a rectangle.