Question

In the diagram, CB and CD are tangents to the circle with centre O. AOC is a straight line and ∠OCB = 34°. ∠ABO equals.

(a) 56°

(b) 28°

(c) 34°

(d) 32°

Answer 1

Correct option is (b) 28°

In △AOB,

OA = OB (Radius of the circle)

Hence, ∠OBA = ∠OAB = x (Isosceles triangle property)

Also, ∠OBC = 90^∘ (Angle between the radius an the tangent)

Now,

In △AOC,

∠ACB + ∠BAC + ∠ABC = 180^∘

34^∘ + x + x + 90^∘ = 180^∘

124^∘ + 2x = 180^∘

x = 28^∘

Thus, ∠ABO = 28^∘