Loci of Points Inspired by Viviani's Theorem
arXiv:1701.07339
Abstract
We 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.
12 pages, 7 figures, to appear in Mathematics Magazine. arXiv admin note: substantial text overlap with arXiv:1410.6442