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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 ______.
Options
60°
70°
80°
90°
Solution
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.
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