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 linear combination of barycenter and circumcenter, its locus over the family is an ellipse.

翻译：我们研究由庞斯莱3期周期(三角形)产生的圆圈的中心力量,这些圆圈来自一对普通的椭圆和三角中心的地缘。我们显示:(一)对于任何同心对,中心在环形或尤勒圆圈方面的力量是无差异的,以及(二)如果3期三角中心在普通的巢状对中是一个固定的中巴和中枢的线性组合,其位于家庭之上的位置是椭圆。