Question 80
Let $ABC$ be a triangle and $D$ and $E$ points on the lines $CA$ and $BA$ such that $CD = AB$, $BE = AC$ and $A$, $D$ and $E$ lie on the same side of $BC$. Let $I$ be the incenter of $ABC$ and let $H$ be a point such that $I$ is the orthocenter of $BCH$. Show that $D$, $E$ and $H$ are collinear.