Question

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

Answer 1

Radius $=3$ (given)

We know $AB=BC$ (tangent draw from a external point to a circle are equal)

$OB=3$ $OC=3$

$\Delta ABO$ is a right angled triangle

$\angle B={90}^0\angle C={90}^0$

$\tan {30}^0=\frac{OB}{AB}=\frac{3}{AD}AD=\frac{3}{\tan {30}^0}=\frac{3}{\frac{1}{\sqrt{3}}}=3\sqrt{3}$