Clark Kimberling, Trilinear distance inequalities for the symmedian
point, the centroid, and other triangle centers,
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.