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Greece Team Selection Test
2009 Greece Team Selection Test
2
2
Part of
2009 Greece Team Selection Test
Problems
(1)
My circumcenter is your barycenter
Source: 2009 Greek TST,Pr.2
5/24/2016
Given is a triangle
A
B
C
ABC
A
BC
with barycenter
G
G
G
and circumcenter
O
O
O
.The perpendicular bisectors of
G
A
,
G
B
,
G
C
GA,GB,GC
G
A
,
GB
,
GC
intersect at
A
1
,
B
1
,
C
1
A_1,B_1,C_1
A
1
,
B
1
,
C
1
.Show that
O
O
O
is the barycenter of
△
A
1
B
1
C
1
\triangle{A_1B_1C_1}
△
A
1
B
1
C
1
.
geometry
circumcircle
perpendicular bisector