Question

In the following, ‘O’ is the centre of the circle. If ∠ACB = 40°, then find ∠OAB.

Answer 1

Given:

O is the centre, ∠ACB = 40°.

∠ACB is an angle at the circumference standing on arc AB.

So the angle at the centre standing on the same arc is:

∠AOB = 2 × ∠ACB = 2 × 40° = 80°.

In triangle AOB, OA = OB (radii of the circle), so it is isosceles.

Therefore, base angles at A and B are equal:

∠OAB = ∠OBA

∠OAB + ∠OBA + ∠AOB = 180°

2∠OAB + 80° = 180°

2∠OAB = 100°

∠OAB = 50°.

∠OAB = 50°.