MathDB
bisector

Source: Balkan MO 2014 G-6

June 10, 2015
geometry

Problem Statement

In △ABC\triangle ABC with AB=ACAB=AC,MM is the midpoint of BCBC,HH is the projection of MM onto ABAB and DD is arbitrary point on the side ACAC.Let EE be the intersection point of the parallel line through BB to HDHD with the parallel line through CC to ABAB.Prove that DMDM is the bisector of ∠ADE\angle ADE.
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