Question

In the given figure, O is the centre of the circle. If $\angle ACB={50}^{\circ }$, find $\angle$OAB.

Answer 1

ANSWER:
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.
∠ AOB = 2 ∠ ACB
= 2 × 50 ° [Given]
∠ AOB = 100 °
...(i)
Let us consider the triangle Δ OAB.
OA = OB (Radii of a circle)
Thus, ∠ OAB = ∠ OBA
In Δ OAB, we have:
∠ AOB + ∠ OAB + ∠ OBA = 180 °
⇒ 100 ° + ∠ OAB + ∠ OAB = 180 °
⇒ 100 ° + 2 ∠ OAB = 180 °
⇒ 2 ∠ OAB = 180 ° – 100 ° = 80 °
⇒ ∠ OAB = 40 °
Hence, ∠ OAB = 40 °