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Canada Contests
Canada National Olympiad
2005 Canada National Olympiad
4
triangle
triangle
Source: Canada 2005
June 26, 2009
geometry
circumcircle
perimeter
inequalities
inradius
geometry proposed
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with circumradius
R
R
R
, perimeter
P
P
P
and area
K
K
K
. Determine the maximum value of:
K
P
R
3
\frac{KP}{R^3}
R
3
K
P
ā
.
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