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Nordic
2004 Nordic
4
4
Part of
2004 Nordic
Problems
(1)
Geometric inequality 1/ab+1/bc+/ca>1/R^2
Source: Nordic MO 2004 Q4
4/20/2013
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the sides and
R
R
R
be the circumradius of a triangle. Prove that
1
a
b
+
1
b
c
+
1
c
a
≥
1
R
2
.
\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\ge\frac{1}{R^2}.
ab
1
+
b
c
1
+
c
a
1
≥
R
2
1
.
inequalities
geometry
circumcircle
inradius
geometry unsolved