We prove that over a generic Poncelet triangle family, the locus of the circumcenter of an inversive triangle is a conic. Additionally, we prove an earlier conjecture: over generic Poncelet triangles, two unique points exist which maintain constant power with respect to the circumcircle and Euler's circle of the family, respectively.

翻译：我们证明，在一般Poncelet三角形族中，反演三角形的外心轨迹是一条圆锥曲线。此外，我们证明了一个早期猜想：在一般Poncelet三角形上，存在两个唯一点，它们分别关于该族的外接圆和欧拉圆保持恒定圆幂。