Problem

Source: Dutch NMO 2015 p5

Tags: algebra, inequalities



Given are (not necessarily positive) real numbers $a, b$, and $c$ for which $|a - b| \ge |c| , |b - c| \ge |a|$ and $|c - a| \ge |b|$ . Prove that one of the numbers $a, b$, and $c$ is the sum of the other two.