Question

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Answer 1

Let us first put the given data in the form of a diagram.

Given data is as follows:

QOR is the diameter.

=

We have to find .

Since QOR is the diameter of the circle, it is a straight line. Therefore,

That is,

But = . Therefore,

Now consider . We have

(Sum of all angles of a triangle will be )

But,

(Since radius will be perpendicular to the tangent at the point of contact)

Therefore,

Therefore, the correct answer to this question is option (c).