RO-TST 2013 Problem 10

Let $\gamma$ a circle and $P$ a point who lies outside the circle. Two arbitrary lines $l$ and $l'$ which pass through $P$ intersect the circle at the points $X$ , $Y$ , respectively $X'$ , $Y'$ , such that $X$ lies between $P$ and $Y$ and $X'$ lies between $P$ and $Y'$ . Prove that the line determined by the circumcentres of the triangles $PXY'$ and $PX'Y$ passes through a fixed point.