Question 12
Prove that a cyclic parallelogram is a rectangle.
Let ABCD be a cyclic parallelogram.
∠A+∠C=180∘ (Opposite angles of a cyclic quadrilateral)
We know that opposite angles of a parallelogram are equal.
∴∠A=∠C and ∠B=∠D
∠A+∠C=180∘
Then ∠A+∠A=180∘
∴2∠A=180∘
⇒∠A=∠C=90∘
Parallelogram ABCD has one of its interior angles as 90∘. Therefore, it is a rectangle.