Question

In Fig below, PQ is tangent at point R of the circle with center O. If ∠TRQ = 30°. Find ∠PRS.

Answer 1

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°