SHARYGIN 2011 Problem 2

Let $ABC$ be a triangle with sides $AB = 4$ , $AC = 6$ . Point $H$ is the projection of vertex $B$ to the bisector of angle $A$ . Find $MH$ , where $M$ is the midpoint of $BC$ .

Official text Sharygin Geometry Olympiad 2011 official paper, page 1. Quoted with source.

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