Question

In the given figure, PQ and PR are tangents drawn from P to a circle with centre O. If ∠OPQ = 35°, then

(a) a= 30°, b= 60°

(b) a= 35°, b = 55°

(c) a= 40°, b = 50°

(d) a= 45°, b = 45°

Answer 1

Consider and . We have,

PO is the common side for both the triangles.

OQ = OR(Radii of the same circle)

PQ = PR(Tangents from an external point will be equal)

Therefore, from SSS postulate of congruent triangles, we have,

Therefore,

That is,

It is given that,

Therefore,

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

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

Therefore, the correct answer is option (b).