NMC 2018 Problem 3

Let $ABC$ be a triangle with $AB < AC$ . Let $D$ and $E$ be on the lines $CA$ and $BA$ , respectively, such that $CD = AB$ , $BE = AC$ , and $A$ , $D$ and $E$ lie on the same side of $BC$ . Let $I$ be the incenter of triangle $ABC$ , and let $H$ be the orthocenter of triangle $BCI$ . Show that $D$ , $E$ , and $H$ are collinear.