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1989 OIM Problems/Problem 3

Revision as of 12:16, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle. Prove: <cmath>\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+...")
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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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