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altitude, bisector and median of HLM, constructed by altitude, median, bisector

Source: Sharygin 2010 Final 8.5

October 2, 2018
geometryaltitudemedianangle bisector

Problem Statement

Let AHAH, BLBL and CMCM be an altitude, a bisectrix and a median in triangle ABCABC. It is known that lines AHAH and BLBL are an altitude and a bisectrix of triangle HLMHLM. Prove that line CMCM is a median of this triangle.
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