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:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 60°.
The angle between a tangent and the radius at the point of tangency is 90°.
So, ∠OPR = 90° and ∠OQR = 90°.
The sum of angles in a quadrilateral is 360°.
In quadrilateral OPRQ, ∠OPR + ∠POQ + ∠OQR + ∠PRQ = 360°
⇒ 90° + 120° + 90° + ∠PRQ = 360°
⇒ 300° + ∠PRQ = 360°
⇒ ∠PRQ = 360° - 300° = 60°
Therefore, the value of ∠PRQ is 60°.