Question

In given figure, O is the centre of a circle and ∠ABC = 45°. Prove that OA ⊥ OC.

Answer 1

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference.
Thus, $\frac{1}{2}\angle \mathrm{AOC}=\angle \mathrm{ABC}$
= 45°
⇒ ∠AOC = 90°
∴ OA ⊥ OC