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Kosovo MO 2009 Grade 12, Problem 3
Kosovo MO 2009 Grade 12, Problem 3
Source: Kosovo MO 2009 Grade 12, Problem 3
June 7, 2021
algebra
inequalities
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be the sides of a triangle, prove that
a
b
+
c
+
b
c
+
a
+
c
a
+
b
<
2
\frac {a}{b+c}+\frac {b}{c+a}+\frac {c}{a+b}<2
b
+
c
a
+
c
+
a
b
+
a
+
b
c
<
2
.
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