Forum Geometricorum, 10 (2010) 135--139.

Abstract: Seven inequalities which appear to be new are derived using Hőlder's inequality and the arithmetic-mean--geometric-

mean inequality. In particular, bounds are found for power sums x^q+y^q+z^q, where x,y,z are the directed distances of a point to the sidelines of a triangle ABC, and the centroid maximizes the product xyz.

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