Question

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to ______.

पर्याय

• 60°

• 70°

• 80°

• 90°

Answer 1

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to 70°.

Explanation:

It is given that TP and TQ are tangents.

Therefore, the radius drawn to these tangents will be perpendicular to the tangents.

Thus, OP ⊥ TP and OQ ⊥ TQ

∠OPT = 90º

∠OQT = 90º

In quadrilateral POQT,

The sum of all interior angles = 360°

∠OPT + ∠POQ + ∠OQT + ∠PTQ = 360°

⇒ 90° + 110° + 90° + ∠PTQ = 360°

⇒ 290° + ∠PTQ = 360°

⇒ ∠PTQ = 360° − 290°

⇒ ∠PTQ = 70°

Hence, the alternative of 70° is correct.