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2004 Croatia National Olympiad
Problem 2
inequality in triangle
inequality in triangle
Source: Croatian MO 2004 3rd Grade P2
April 8, 2021
inequalities
geometric inequality
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are the sides and
α
,
β
,
γ
\alpha,\beta,\gamma
α
,
β
,
γ
the corresponding angles of a triangle, prove the inequality
cos
α
a
3
+
cos
β
b
3
+
cos
γ
c
3
≥
3
2
a
b
c
.
\frac{\cos\alpha}{a^3}+\frac{\cos\beta}{b^3}+\frac{\cos\gamma}{c^3}\ge\frac3{2abc}.
a
3
cos
α
+
b
3
cos
β
+
c
3
cos
γ
≥
2
ab
c
3
.
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