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Ineq 2

Source: Indian RMO 2005 Problem 3

February 28, 2006
inequalities

Problem Statement

If a,b,ca,b,c are positive three real numbers such that ∣a−b∣≥c,∣b−c∣≥a,∣c−a∣≥b| a-b | \geq c , | b-c | \geq a, | c-a | \geq b . Prove that one of a,b,ca,b,c is equal to the sum of the other two.
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