In the given figure, O is the centre of the circle. If ∠ACB = 50°, find ∠OAB.

Open in App

Solution

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 ΔOAB.
OA = OB (Radii of a circle)
Thus, ∠OAB = ∠OBA
In ΔOAB, we have:
∠AOB + ∠OAB + ∠OBA = 180°
⇒ 100° + ∠OAB + ∠OAB = 180°
⇒ 100° + 2∠OAB = 180°
⇒ 2∠OAB = 180° – 100° = 80°
⇒ ∠OAB = 40°
Hence, ∠OAB = 40°

Suggest Corrections

Similar questions

In the given figure, O is the centre of the circle. If $∠ A C B = 50^{\circ}$ , find $∠$ OAB.

In the figure, O is the centre of the circle. If $∠ A P B = 50^{o}$ , find $∠ A O B a n d ∠ O A B$ .

In the given figure, O is the centre of a circle. If $∠ O A B = 40^{\circ}$ and C is a point on the circle then $∠ A C B = ?$

(a) $40^{\circ}$

(b) $50^{\circ}$

(d) $100^{\circ}$

Join BYJU'S Learning Program