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My circumcenter is your barycenter

Source: 2009 Greek TST,Pr.2

May 24, 2016

geometrycircumcircleperpendicular bisector

Problem Statement

Given is a triangle

ABC

with barycenter

G

and circumcenter

O

.The perpendicular bisectors of

GA,GB,GC

intersect at

A_1,B_1,C_1

.Show that

O

is the barycenter of

\triangle{A_1B_1C_1}

.

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