Australian AMC 2014 - Senior Question 24

Question 24

In the diagram, $QS,RT,SV$ are tangents to the circle; the right angle at $S$ is marked. If $RS=1$ metre and $\angle SRT=60^\circ$, what is the circle diameter in metres?

Question illustration

$3+\sqrt3$
4
$2\sqrt3+2$
$3\sqrt3$
$9/2$