Question

In figure, if ∠OAB = 40°, then ∠ACB equals

(a) 50°

(b) 40°

(c) 60°

(d) 70°

Answer 1

Answer is (a) 50°

∵ OA = OB (radius of circle)

∴ ∠OAB = ∠OBA (angles opposite to equal sites)

⇒ ∠OBA = 40°

In right angled ∆OAB

∠OAB + ∠OBA + ∠AOB = 180°

⇒ 40° + 40° + ∠AOB = 180°

⇒ ∠AOB = 180° – 80°

⇒ ∠AOB = 100°

We know that

∠ACB = \(\frac { 1 }{ 2 }\)∠AOB

= \(\frac { 1 }{ 2 }\) x 100° = 50°