The Total solution for NCERT class 6-12
Prove that a cyclic parallelogram is a rectangle.
Let ABCD bea cyclic parallelogram.
∠A + ∠C = 180° (Opposite angles of a cyclic quadrilateral) … (1)
We know that opposite angles of a parallelogram are equal.
∴ ∠A = ∠C and ∠B = ∠D
From equation (1),
∠A + ∠C = 180°
⇒ ∠A + ∠A = 180°
⇒ 2 ∠A = 180°
⇒ ∠A = 90°