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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 = ?
Options
40°
50°
60°
70°
MCQ
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Solution
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°
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