Question:
If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 60°, then OP = a√3.
Solution:
True
From point $P$, two tangents are drawn.
Given, $O T=a$
Also line $O P$ bisects the $\angle R P T$.
$\angle T P O=\angle R P O=30^{\circ}$
Also, $O T \perp P T$
In right angled $\triangle O T P$,
$\sin 30^{\circ}=\frac{O T}{O P}$
$\Rightarrow$ $\frac{1}{2}=\frac{a}{O P}$
$\Rightarrow$ $O P=2 a$