ZA-SAMO 2013 Problem 6

Let $ABC$ be an acute-angled triangle with $AC \neq BC$ , and let $O$ be the circumcentre and $F$ the foot of the altitude through $C$ . Furthermore, let $X$ and $Y$ be the feet of the perpendiculars dropped from $A$ and $B$ respectively to (the extension of) $CO$ . The line $FO$ intersects the circumcircle of $FXY$ a second time at $P$ . Prove that $OP<OF$ .