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Geometrical Inequality

Source: KöMaL A. 809

March 23, 2022
inequalitiesgeometrykomal

Problem Statement

Let the lengths of the sides of triangle ABCABC be denoted by a,b,a,b, and c,c, using the standard notations. Let GG denote the centroid of triangle ABC.ABC. Prove that for an arbitrary point PP in the plane of the triangle the following inequality is true: a⋅PA3+b⋅PB3+c⋅PC3≥3abc⋅PG.a\cdot PA^3+b\cdot PB^3+c\cdot PC^3\geq 3abc\cdot PG.Proposed by János Schultz, Szeged
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