1989 OIM Problems/Problem 3

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Problem

Let $a$, $b$, and $c$ be the longitudes of the sides of a triangle. Prove: \[\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe4.htm