Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

Tags: geometry, angle bisector, orthocenter, collinear



Let $H$ be an orhocenter of an acute triangle $ABC$ and $M$ midpoint of side $BC$. If $D$ and $E$ are foots of perpendicular of $H$ on internal and external angle bisector of angle $\angle BAC$, prove that $M$, $D$ and $E$ are collinear