AHSME 1980 Problem 5

If $AB$ and $CD$ are perpendicular diameters of circle $Q$, $P$ in $\overline{AQ}$, and $\measuredangle QPC = 60^\circ$, then the length of $PQ$ divided by the length of $AQ$ is

$\text{(A)} \ \frac{\sqrt{3}}{2} \text{(B)} \ \frac{\sqrt{3}}{3} \text{(C)} \ \frac{\sqrt{2}}{2} \text{(D)} \ \frac12 \text{(E)} \ \frac23$