Loci of Points Inspired by Viviani′s Theorem
Elias Abboud · Mathematics Magazine · 2017
SummaryWe consider loci of points such that their sum of distances or sum of squared distances to each of the sides of a given triangle is constant. These loci are inspired by Viviani′s theorem and its extension. The former locus is a line segment or the whole triangle and the latter locus is an ellipse.