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SNAP 2014 Question-31

Q.) 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
tangent-question1)\frac { 3 }{ 2 } \sqrt { 2 } cm
2)6 cm
3)3 cm
4)3\sqrt { 3 } cm

Solution :
We know that tangent is always perpendicular to the radius of circle , so in triangle OPT ,
\tan { \theta =\frac { P }{ b } \quad }

In the given triangle above,

\tan { 30=\frac { OP }{ PT } \quad }

=> PT = OPtan30 = 3 X \sqrt { 3 } = 3\sqrt { 3 }

Now,length of two tangents from an external same point to a circle is equal to each other.

Hence , length of each tangent =3\sqrt { 3 }

Hence , Option(4)


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