Problem

Source: Canada RepĂȘchage 2020/6 CMOQR

Tags: concurrency, concurrent, geometry, pentagon, orthocenter



In convex pentagon $ABCDE, AC$ is parallel to $DE, AB$ is perpendicular to $AE$, and $BC$ is perpendicular to $CD$. If $H$ is the orthocentre of triangle $ABC$ and $M$ is the midpoint of segment $DE$, prove that $AD, CE$ and $HM$ are concurrent.