State 'True' or 'False' and give reasons for your answer.
If the angle between two tangents drawn from a point $P$ to a circle of radius $a$ and center $O$ is $60^{\circ}$,then $OP = a\sqrt{3}$.

(B) False.
Let $PT$ and $PR$ be the two tangents drawn from point $P$ to the circle with center $O$ and radius $a = OT = OR$.
The line $OP$ bisects the angle between the tangents,so $\angle TPO = \angle RPO = \frac{60^{\circ}}{2} = 30^{\circ}$.
Since the radius is perpendicular to the tangent at the point of contact,$\angle OTP = 90^{\circ}$.
In the right-angled triangle $\Delta OTP$,we have:
$\sin(\angle TPO) = \frac{OT}{OP}$
$\sin(30^{\circ}) = \frac{a}{OP}$
$\frac{1}{2} = \frac{a}{OP}$
$OP = 2a$.
Therefore,the statement $OP = a\sqrt{3}$ is False.