In Fig. 10.6, if OAB = 40 �, then ACB is equal to:

Question

Philoid · Accepted Answer

In triangle AOB,

AO = OB = Radius

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

Using the angle sum property of triangle, sum of all angles of a triangle is 180°,

∴ ∠OAB + ∠OBA + ∠AOB = 180°

⇒ 40° + 40° + ∠AOB = 180°

⇒ ∠AOB = 180° - 40° - 40°

⇒ ∠AOB = 100°

By theorem “The angle subtended by an arc at the center of a circle is twice the angle subtended by it at remaining part of the circle”, we have:

∠AOB = 2 × ∠ACB

∠ACB = ∠AOB/2

= 100°/2

∴ ∠ACB = 50°