MathDB

Collinear

Source: All Russian Mathematical Olympiad 2008. 9.3

June 13, 2008

geometryEulercircumcirclevectorgeometry proposed

Problem Statement

In a scalene triangle

ABC, H

and

M

are the orthocenter an centroid respectively. Consider the triangle formed by the lines through

A,B

and

C

perpendicular to

AM,BM

and

CM

respectively. Prove that the centroid of this triangle lies on the line

MH