Let $ABC$ be a triangle with sides $AB = 4$ and $AC = 6$. Point $H$ is the projection of vertex $B$ to the bisector of angle $A$. Find $MH$, where $M$ is the midpoint of $BC$.
Source: 2011 Sharygin Geometry Olympiad #2
Tags: geometry unsolved, geometry
Let $ABC$ be a triangle with sides $AB = 4$ and $AC = 6$. Point $H$ is the projection of vertex $B$ to the bisector of angle $A$. Find $MH$, where $M$ is the midpoint of $BC$.