Question

In the given figure, if TP and TQ are tangents drawn from an external point T to a circle with centre O such that ∠TQP = 60°, then ∠OPQ =

(a) 25°

(b) 30°

(c) 40°

(d) 60°

Answer 1

Consider .

We have,

TP = TQ(Tangents from an external point will be equal)

We know that angles opposite to equal sides will be equal. Therefore,

It is given that,

Therefore,

We know that the radius will always be perpendicular to the tangent at the point of contact. Therefore,

Hence,

That is,

We have found that,

Therefore,

Therefore, the correct answer is option (b).