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2016 Latvia National Olympiad 3rd Round Grade11Problem2

Source:

July 22, 2016
geometrycircumcircle

Problem Statement

An acute triangle ABCABC (AB>ACAB > AC) has circumcenter OO, but DD is the midpoint of BCBC. Circle with diameter ADAD intersects sides ABAB and ACAC in EE and FF respectively. On segment EFEF pick a point MM so that DM∥AODM \parallel AO. Prove that triangles ABDABD and FDMFDM are similar.
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