Question 46
Let $ABC$ be a triangle and $I$ the center of its inscribed circle. Let $D$ and $E$ be the feet of the angle bisectors from $B$ and $C$. Let $X$ be the intersection of the reflections of $(AB)$ and $(AC)$ across $(CE)$ and $(BD)$ respectively. Show that the lines $(XI)$ and $(BC)$ are perpendicular.