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geom ineq lp

Source: Laurentiu Panaitopol,Romania, TST 1990

August 10, 2005
inequalitiesfunctiongeometrycircumcircleinequalities proposed

Problem Statement

Prove that in any triangle ABCABC the following inequality holds: a2b+c−a+b2a+c−b+c2a+b−c≥33R. \frac{a^{2}}{b+c-a}+\frac{b^{2}}{a+c-b}+\frac{c^{2}}{a+b-c}\geq 3\sqrt{3}R. Laurentiu Panaitopol
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