MathDB

AB

and

CD

are perpendicular diameters of circle

Q

P

\overline{AQ}

, and

\measuredangle QPC = 60^\circ

, then the length of

PQ

divided by the length of

AQ

is [asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair A=(-1,0), B=(1,0), C=(0,1), D=(0,-1), Q=origin, P=(-0.5,0); draw(P--C--D^^A--B^^Circle(Q,1)); label("

A

", A, W); label("

B

", B, E); label("

C

", C, N); label("

D

", D, S); label("

P

", P, S); label("

Q

", Q, SE); label("

60^\circ

", P+0.0.5*dir(30), dir(30));[/asy]

<span class='latex-bold'>(A)</span> \ \frac{\sqrt{3}}{2} \qquad <span class='latex-bold'>(B)</span> \ \frac{\sqrt{3}}{3} \qquad <span class='latex-bold'>(C)</span> \ \frac{\sqrt{2}}{2} \qquad <span class='latex-bold'>(D)</span> \ \frac12 \qquad <span class='latex-bold'>(E)</span> \ \frac23

Problem Statement