If PQ and PR be the two tangents to a circle with centre

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If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120°, then ∠POQ is :

1. 90°
2. 45°
3. 30°
4. 60°

Correct Option: C

As per the given in question , we draw a figure of circle in which PQ and PR be the two tangents

PQ = PR (Tangents from the same exterior point)
Given , ∠QPR = 120°

∠OPQ = ∠OPR =	120°	= 60°
	2

∴ OQ ⊥ PQ (Tangent)
From ∆OQP ,
∴ ∠OQP = 90°
∴ ∠POQ + ∠OPQ = 90°
∴ ∠POQ = 90° – 60° = 30°