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in Mathematics by (45.2k points)
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TP and TQ are two tangents drawn from an external point T to a circle whose centre is O such that \(\angle\)POQ = 120°. Then the value of \(\angle\)OTP is 

(A) 40°

(B) 30°

(C) 50°

(D) 60°

2 Answers

+1 vote
by (45.9k points)
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Best answer

Correct option is (B) 30°

TP and TO are two tangents drawn from an external point T to a circle

Given that \(\angle P O Q=120^{\circ}\)

\(\angle O P T=\angle O QT=90^{\circ}\)

[\(\because\)A tangent at any point of a Circle is perpendicular to the radius at the point of contact]

\(\angle P O T =\frac{1}{2} \angle P O Q \)

\(=\frac{1}{2} \times 120^{\circ} \)

\(=60^{\circ}\)

In \(\triangle P O T\),

\(\angle O P T+\angle P O T+\angle O T P =180^{\circ}\)

\(90^{\circ}+60^{\circ}+\angle O T P =180^{\circ}\)

\(\angle O T P =180^{\circ}-150^{\circ}\)

\(=30^{\circ}\)

0 votes
by (15.5k points)
edited by

Bhagvad, hello

The question is slightly confusing because TO would not be a tangent if T was an external point and O was the center of the circle.  Below is my attempt, is I interpreted the question correctly I believe that the correct answer is: (B) 30o

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