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Projection of a vertex to an angle bisector

Source: 2011 Sharygin Geometry Olympiad #2

May 22, 2014
geometry unsolvedgeometry

Problem Statement

Let ABCABC be a triangle with sides AB=4AB = 4 and AC=6AC = 6. Point HH is the projection of vertex BB to the bisector of angle AA. Find MHMH, where MM is the midpoint of BCBC.
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