Question 47
In circle $O,$ the midpoint of radius $\overline{OX}$ is $Q;$ at $Q,$ $\overline{AB}\perp\overline{XY}.$ The semicircle with $\overline{AB}$ as diameter intersects $\overline{XY}$ in $M.$ Line $AM$ intersects circle $O$ in $C,$ and line $BM$ intersects circle $O$ in $D.$ Line $AD$ is drawn. Then, if the radius of circle $O$ is $r,$ $AD$ is:
