Question

In the given figure, O is the centre of the circle and $\angle \text{AOB}={70}^{\circ }$.

Calculate the values of (i) $\angle \text{OCA}\left(ii\right)\angle \text{OAC}.$

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
⇒∠OCA=∠AOB/2=70°/2=35°
(ii)
OA = OC (Radii of a circle)
∠ OAC = ∠ OCA [Base angles of an isosceles triangle are equal]
= 35 °