If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120°$,…

Question

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 :

Accepted Answer

## 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°.

Mathematics — CBSE Class 10 board question