Q1. [1] § 10.1 Introduction § 10.2 Tangent to a Circle
If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120°$, then $\angle PTQ$ is equal to :
- (a) $60°$
- (b) $70°$
- (c) $80°$
- (d) $90°$
Previously asked in CBSE board exam
2026 30/1/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
(a) 60°
Since OP ⊥ TP and OQ ⊥ TQ (radius ⊥ tangent), in quadrilateral OPTQ:
∠PTQ = 360° − 90° − 90° − 120° = 60°.
Explanation
In quadrilateral OPTQ, the four angles sum to 360°. Both ∠OPT and ∠OQT = 90° (Theorem 10.1). So ∠PTQ = 360° − 90° − 90° − ∠POQ = 360° − 90° − 90° − 120° = 60°. Note: the textbook example uses ∠POQ = 110° giving 70°; here ∠POQ = 120° gives 60°.
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