Problem

Source: Kosovo MO 2012 Grade 10, Problem 2

Tags: geometry, Inequality



Let $a,b,c$ be the lengths of the sides of a triangle. Prove that, $\left|\frac {a}{b}+\frac {b}{c}+\frac {c}{a}-\frac {b}{a}-\frac {c}{b}-\frac {a}{c}\right|<1$