Question 5If $AB$ and $CD$ are perpendicular diameters of circle $Q,$ $P$ in $AQ,$ and $\angle QPC=60^\circ,$ then the length of $PQ$ divided by the length of $AQ$ is $\frac{\sqrt3}{2}$$\frac{\sqrt3}{3}$$\frac{\sqrt2}{2}$$\frac12$$\frac23$
