3 problems

Let $\mathcal{X}$ be a triangle center, and consider its locus as the triangle ranges over Poncelet 3-periodics in a concentric pair of non-axis-aligned ellipses. Elliptic-locus ch…

Consider a non-concentric, non-axis-aligned pair of ellipses admitting Poncelet 3-periodics. For each 3-periodic, let its circumcircle and Euler circle be the circles associated wi…

Let a generic concentric pair consist of an outer ellipse and an inner ellipse admitting Poncelet 3-periodics. Let $X_3$ and $X_5$ denote the circumcenter and Euler center of a 3-p…