4 problems

Let $\mathcal{L}_7$ and $\mathcal{L}_8$ denote the loci of the Gergonne point $X_7$ and Nagel point $X_8$, respectively, in a Poncelet triangle family. The pair of Poncelet conics…

Let $X_1$ be the incenter of a Poncelet triangle, and consider its locus as the triangle varies in a family interscribed between two conics. The pair is confocal when the two Ponce…

Let $X_7$ and $X_8$ be the Gergonne and Nagel points, respectively, of a Poncelet triangle family, and let their loci be denoted by $\mathcal{L}_7$ and $\mathcal{L}_8$. A Poncelet-…

Let a pair of conics admit a family of Poncelet 3-periodics, and consider the locus traced by the incenter $X_1$ and by the excenters of the triangles in that family. Confocality c…