Problem

Source: Ukrainian mathematical olympiad 2018 11.2

Tags: geometry



In acute-angled triangle $ABC$, $AH$ is an altitude and $AM$ is a median. Points $X$ and $Y$ on lines $AB$ and $AC$ respectively are such that $AX=XC$ and $AY=YB$. Prove that the midpoint of $XY$ is equidistant from $H$ and $M$. Proposed by Danylo Khilko