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IberoAmerican
1989 IberoAmerican
3
Side lengths of a triangle inequality
Side lengths of a triangle inequality
Source: IberoAmerican 1989 Q3
November 27, 2010
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be the side lengths of a triangle. Prove that:
a
−
b
a
+
b
+
b
−
c
b
+
c
+
c
−
a
c
+
a
<
1
16
\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}
a
+
b
a
−
b
+
b
+
c
b
−
c
+
c
+
a
c
−
a
<
16
1
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