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

Question

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

Philoid · Accepted Answer

Given: ∠OAB = 40°

Consider ΔAOB

Here,

OA = OB (radius)

∠OBA = ∠OAB = 40° (angles opposite to equal sides are equal)

By angle sum property

∠OBA + ∠OAB + ∠AOB = 180°

40° + 40° + ∠AOB = 180°

∠AOB = 180° — 40° — 40° = 100°

We know that,

∠AOB = 2× ∠ACB

∠AOB = ∠ACB

×100° = ∠ACB

∠ACB = 50°

∴∠ACB = 50°