OME 2009 Problem 6

Inside a circle of center $O$ and radius $r$ , take two points $A$ and $B$ symmetrical about $O$ . We consider a variable point $P$ on the circle and draw the chord $\overline{PP'}\perp \overline{AP}$ . Let $C$ is the symmetric of $B$ about $\overline{PP'}$ ( $\overline{PP}'$ is the axis of symmetry) . Find the locus of point $Q = \overline{PP'}\cap\overline{AC}$ when we change $P$ in the circle.