Question

If the pair of straight lines $xy\sqrt{3}-x^2=0$ is tangent to the circle at $P$ and $Q$ from origin $O$ such that area of smaller sector formed by $CP$ and $CQ$ is $3\pi .$ sq.units, where $C$ is the centre of circle, then $OP$ equals to

• A. $\frac{\left(3\sqrt{3}\right)}{2}$
• B. $3\sqrt{3}$
• C. $3$
• D. $\sqrt{3}$

Answer 1

The correct option is B $3\sqrt{3}$

$\tan {30}^0=\frac{r}{OP}\Rightarrow OP=r\sqrt{3}$
$\therefore r^2\frac{1}{2}\frac{2\pi }{3}=3\pi \Rightarrow r=3\therefore OP=3\sqrt{3}$