In the given figure, O is the centre of a circle, ∠ACB = 40°. Find ∠OAB.

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

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Similar questions

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

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) $100^{\circ}$

∠

^{o}

∠

^{o}

∠

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