Question

In the given figure, if PR is tangent to the circle at P and Q is the centre of the circle, then ∠POQ =

(a) 110°

(b) 100°

(c) 120°

(d) 90°

Answer 1

We know that the radius is always perpendicular to the tangent at the point of contact.

Therefore, we have,

It is given that,

That is,

Now, consider. We have,

OP = OQ (Radii of the same circle)

Since angles opposite to equal side will be equal in a triangle, we have,

We know that sum of all angles of a triangle will be equal to .

Therefore,

The correct answer is option (c).