Question

In the given diagram, O is the center of the circle and CD is a tangent. ∠CAB and ∠ACD are supplementary to each other. ∠OAC = 30°. Find the value of ∠OCB?

(a) 30° 

(b) 20° 

(c) 60° 

(d) None of these

Answer 1

Answer : (a) 30º 

∠OCD = 90° (Tangent CD ⊥ Radius OC)

∠OCA = ∠OAC = 30° (OA = OC, radii)

∠ACD = ∠OCD + ∠OCA = 90° + 30° = 120°

∠BAC = 180° – 120° = 60° (Given ∠ACD and ∠BAC are supp.)

⇒ ∠BCD = ∠BAC = 60° (Angles in alternate segment are equal)

∠OCB = ∠OCD – ∠BCD = 90° – 60° = 30°