1989 OIM Problems/Problem 2
Problem
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Let 
, 
, and 
be the longitudes of the sides of a triangle. Prove:
![\[\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}\]](http://latex.artofproblemsolving.com/8/1/5/815e94b144f496e813104e2bf97099d86c48b775.png)
Solution
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