Question

In the given figure, O is the canter of the circle and ∠AOB = 70°.
Calculate the values of (i) ∠OCA, (ii) ∠OAC.

Answer 1

(i)
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, ∠AOB = 2∠OCA
$\Rightarrow \angle OCA=\left(\frac{\angle AOB}{2}\right)=\left(\frac{70°}{2}\right)=35°$

(ii)
OA = OC (Radii of a circle)
∠OAC = ∠OCA [Base angles of an isosceles triangle are equal]
= 35°