Question

If two tangents inclined at an angle ${60}^{\circ }$ 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. $6cm$
• C. $3cm$
• D. $3\sqrt{3}cm$

Answer 1

Answer: (D)

$3\sqrt{3}cm$

Let PA and PB are the tangents on the circle. $\angle APB=60$. the radius of the circle with center at O be 3 cm.
The two tangents drawn to a circle from an external point are equally inclined to the segment joining the center to the point.
Thus, $\angle APO={30}^{\circ }$
In $△OAP$
$\angle OAP={90}^{\circ }$ ...(Angle between tangent and radius)
$\tan 30=\frac{1}{\sqrt{3}}=\frac{OA}{AP}$
$PA=3\sqrt{3}$