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If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm,then length of each tangent is equal to

(A) \frac{3}{2}\sqrt{3}cm                 (B) 6 cm                      (C) 3 cm                      (D) 3\sqrt{3}cm

Answers (1)

Answer (D) 3\sqrt{3}cm
According to question

Given OQ = OR = 3 cm (Radius)
\angle P= 60^{\circ}
Draw line OP which bisect \angle P . That is \angle OPQ= 30^{\circ}

\angle OPR= 30^{\circ}
In \bigtriangleup OPQ
\tan \theta = \frac{P}{B}
\tan 30^{\circ} = \frac{3}{PQ}
\frac{1}{\sqrt{3}}= \frac{3}{PQ}
PQ= 3\sqrt{3}
Here PQ = PR
Hence , PQ = PR= 3\sqrt{3}

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