MathDB
Geometry problem

Source: EGMO 2018 Moldova TST

February 11, 2018
geometry

Problem Statement

Let △ABC\triangle ABC be an acute triangle.OO denote its circumcenter.Points DD,EE,FF are the midpoints of the sides BCBC,CACA,and ABAB.Let MM be a point on the side BCBC . AM∩EF={N} AM \cap EF = \big\{ N \big\} . ON∩(ODM)={P}ON \cap \big( ODM \big) = \big\{ P \big\} Prove that M′M' lie on (DEF)\big(DEF\big) where M′M' is the symmetrical point of MM thought the midpoint of DPDP.
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