Problem

Source: 2018 China North Mathematical Olympiad Grade 10 Test 2 P2

Tags: geometry, China, circumcircle



Let $H$ be the orthocenter of triangle $ABC$. Let $D$ and $E$ be points on $AB$ and $AC$ such that $DE$ is parallel to $CH$. If the circumcircle of triangle $BDH$ passes through $M$, the midpoint of $DE$, then prove that $\angle ABM=\angle ACM$