Question

In the given figure, O is the centre of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that ∠SQL = 50° and ∠SRM = 60°. Then, ∠QSR = ?

पर्याय

• 40°

• 50°

• 60°

• 70°

Answer 1

70°

Explanation:

Since PQL is a tangent and OQ is a radius, so ∠OQL = 90°.

∴ ∠OQS = 90° – 50°

∴ ∠OQS = 40°

Now, OQ = OS

⇒ ∠OSQ = ∠OQS

⇒ ∠OSQ = 40°

Similarly, ∠ORS = 90° – 60°

∠ORS = 30°

And OR = OS

⇒ ∠OSR = ∠ORS

⇒ ∠OSR = 30°

∴ ∠OSR = ∠OSQ + ∠OSR

= 40° + 30°

= 70°