5 problems

Polar Harmonic-family conjecture. The sum of half-angle tangents is conserved for the polar image of the Harmonic family, for all $N>3$.

Stationary-orthocenter classification conjecture. A Poncelet triangle family maintains $X_4$ stationary only if the conics are configured as focal-$X_4$, MacBeath, or Dual.

Let $\mathcal{T}_{\circ}$ be the Poncelet family whose circumcircle is constrained by the circular caustic, and let $\Gamma$ denote the line associated with the circumcircle-incent…

Let $\mathcal{T}$ be the family of Poncelet triangles, and let $\mathcal{E}_c$ be the inner Poncelet caustic. Consider the envelope of the circumcircle as the triangles range over…

Let $T$ be a reference triangle, and let $T'$ be its $X_{55}$-reflection triangle. The six vertices of the P-hyperbolas of $T'$ passing through $X_{55}$ of $T$ are the six points a…