If RP and RQ are two tangents to a circle with centre O such that ∠POQ = 120°, where P and Q are the points on the circle and R is a point outside the circle then ∠PRQ is equal to:

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 2)
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  1. 90°
  2. 75°
  3. 60°
  4. 45°

Answer (Detailed Solution Below)

Option 3 : 60°
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Detailed Solution

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Given:

RP and RQ are the two tangents of a circle.

∠POQ = 120°

Concept used:

The tangent makes a right angle with the radius of a circle at the point of contact.

The sum of all angles of a quadrilateral = 360°

Calculation:

   F2 SSC PriyaS 13-2-24 D27

In the figure:

OP ⊥ PR and OQ ⊥ RQ

∠OPR = ∠OQR = 90°

In quadrilateral POQR

⇒ ∠OPR + ∠OQR + ∠POQ + ∠PRQ = 360

​ 90 + 90 + 120 + ∠PRQ = 360

⇒ ∠PRQ = (360 - 300) = 60°

∴ The correct answer is 60°.

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