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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

1)$\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)