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\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}< 2 when a,b,c sidelengths

Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p1b

February 11, 2020
inequalitiesGeometric Inequalities

Problem Statement

Given a triangle with sides of lengths a,b,ca,b,c, prove that ab+c+bc+a+ca+b<2\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}< 2.
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