Question

In the given figure, AB is a chord of the circle with centre O and PQ is a tangent at point B of the circle. If ∠AOB = 110°, then ∠ABQ is

(a) 45°

(b) 70°

(c) 55°

(b) 35°

Answer 1

Correct option is (c) 55°

Given, ∠AOB = 110^∘

In △AOB

OA = OB (Radius of the circle)

Thus, ∠OAB = ∠OBA (Isosceles triangle property)

Sum of angles of the triangle = 180^∘

∠AOB + ∠OAB + ∠OBA = 180^∘

110 + 2∠OBA = 180^∘

∠OBA = 35^∘

Since, PQ is a tangent touching the circle at B.

Thus, ∠OBQ = 90^∘

Now, ∠ABQ + ∠OBA = 90^∘

∠ABQ + 35° = 90^∘

∠ABQ = 55^∘