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19/06/2021 11:26 am
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In 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°
1 Answer
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19/06/2021 11:28 am
Correct option:(B) 70°
Explanation:
From the question, it is clear that OP is the radius of the circle to the tangent PT and OQ is the radius to the tangents TQ.
So, OP ⊥ PT and TQ ⊥ OQ
∴∠OPT = ∠OQT = 90°
Now, in the quadrilateral POQT, we know that the sum of the interior angles is 360°
So, ∠PTQ+∠POQ+∠OPT + ∠OQT = 360°
Now, by putting the respective values we get,
∠PTQ +90°+110°+90° = 360°
∠PTQ = 70°
So, ∠PTQ is 70°