Question

In the given figure, APB is a tangent to a circle with centre O at point P. If ∠QPB = 50°, then the measure of ∠POQ is

(a) 100°

(b) 120°

(c) 140°

(d) 150°

Answer 1

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

Therefore,

That is,

It is given that,

Therefore, we have,

Now, consider . We have,

OP = OQ(Radii of the same circle)

Since angles opposite to equal sides will be equal, we have,

We have found that,

Therefore,

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

The correct answer is option (a).