Invariant center power and elliptic loci of Poncelet triangles
In this paper the authors studied about the center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. They proved that for any concentric pair, the power of the center with respect to either circumcircle or Euler's circle is invariant, and if a triangle center of a 3-periodic in a generic nested pair is a fixed linear combination of barycenter and circumcenter, its locus over the family is an ellipse. In the last section of the article the authors conclude with three conjectures.
scientific article; zbMATH DE number 7671520
scientific article