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Balkan MO
1996 Balkan MO
1
1
Part of
1996 Balkan MO
Problems
(1)
Geometrical inequality involving the centroid and circumcent
Source: Balkan MO 1996, Problem 1
4/24/2006
Let
O
O
O
be the circumcenter and
G
G
G
be the centroid of a triangle
A
B
C
ABC
A
BC
. If
R
R
R
and
r
r
r
are the circumcenter and incenter of the triangle, respectively, prove that
O
G
≤
R
(
R
−
2
r
)
.
OG \leq \sqrt{ R ( R - 2r ) } .
OG
≤
R
(
R
−
2
r
)
.
Greece
inequalities
geometry
circumcircle
incenter
Euler
inequalities proposed