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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

(A) 60 (B) 70

(C) 80 (D) 90

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Solution

It is given that TP and TQ are tangents.

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

Thus, OP ⊥ TP and OQ ⊥ TQ

∠OPT = 90º

∠OQT = 90º

In quadrilateral POQT,

Sum of all interior angles = 360

∠OPT + ∠POQ +∠OQT + ∠PTQ = 360

⇒ 90+ 110º + 90 +PTQ = 360

PTQ = 70

Hence, alternative (B) is correct.


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