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an altitude of an acute triangle

Source: All-Russian 2007

May 4, 2007

geometrycircumcircleAsymptotepower of a pointradical axisperpendicular bisectorgeometry proposed

Problem Statement

Let

ABC

be an acute triangle. The points

M

and

N

are midpoints of

AB

and

BC

respectively, and

BH

is an altitude of

ABC

. The circumcircles of

AHN

and

CHM

meet in

P

where

P\ne H

. Prove that

PH

passes through the midpoint of

MN

. V. Filimonov