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Triangles have the same centroid

Source: SAMO Senior Round 3 2012 Problem 5

September 6, 2012

geometrycircumcirclegeometric transformationhomothetyratioEulergeometry unsolved

Problem Statement

Let

ABC

be a triangle such that

AB\neq AC

. We denote its orthocentre by

H

, its circumcentre by

O

and the midpoint of

BC

D

. The extensions of

HD

and

AO

meet in

P

. Prove that triangles

AHP

and

ABC

have the same centroid.