Algebra · Absolute value · Inequalities · Equality cases
Real numbers \(a\), \(b\), \(c\) satisfy the three inequalities
\[ |b - c| \ge |a|, \qquad |c - a| \ge |b|, \qquad |a - b| \ge |c|. \]
Prove that one of the numbers \(a\), \(b\), \(c\) is equal to the sum of the other two.
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Serbian Municipal Competition 2014, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source