Question 182
Let $ABC$ be a scalene acute triangle with incentre $I$ and circumcentre $O$. Let $AI$ cross $BC$ at $D$. On circle $ABC$, let $X$ and $Y$ be the mid-arc points of $ABC$ and $BCA$, respectively. Let $DX$ cross $CI$ at $E$ and let $DY$ cross $BI$ at $F$. Prove that the lines $FX$, $EY$ and $IO$ are concurrent on the external bisector of $\angle BAC$.