  We study 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. We show that (i) for any concentric pair, the power of the
center with respect to either circumcircle or Euler's circle is invariant, and
(ii) if a triangle center of a 3-periodic in a generic nested pair is a fixed
affine combination of barycenter and circumcenter, its locus over the family is
an ellipse.
