2 problems

Let a pair of ellipses admit Poncelet 3-periodics, and let $X_1$ denote the incenter of a member of the family. The pair is confocal when its two ellipses share the same foci. Ince…

Let a pair of ellipses admit Poncelet 3-periodics, and consider the loci of the excenters of the triangles in the family. The pair is poristic when the associated Poncelet family h…