Question
Download Solution PDFIf 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
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°.
Last updated on Jul 12, 2025
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