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Question
In Fig below, PQ is tangent at point R of the circle with center O. If ∠TRQ = 30°. Find
∠PRS.
Solution
Given ∠TRQ = 30°.
At point R, OR ⊥ RQ.
∠ORQ = 90°
⇒ ∠TRQ + ∠ORT = 90°
⇒ ∠ORT = 90° − 30° = 60°
ST is diameter, ∠SRT = 90° [∵ Angle in semicircle = 90°]
∠ORT + ∠ SRO = 90°
∠SRO + ∠PRS = 90°
∠PRS = 90° − 30° = 60°
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