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Triangle Inequality.

Source: Chinese Northern Mathematical Olympiad 2007

August 5, 2007

inequalitiesgeometric inequalityinequalities proposedChinaHigh school olympiad

Problem Statement

Let

a,\, b,\, c

be side lengths of a triangle and

a+b+c = 3

. Find the minimum of

a^{2}+b^{2}+c^{2}+\frac{4abc}{3}