5 papers
Conic locus of inversive Poncelet circumcenter and two points of invariant circle power
Ronaldo Garcia, Shmuel Mark Helman, Dan Reznik
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…
Harmonious loci of Poncelet triangles about the incircle and their degeneracies
Mark Helman, Ronaldo A. Garcia, Dan Reznik
We tour several Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle, including loci of triangle centers and envelopes of key objects.…
Four special Poncelet triangle families about the incircle
Ronaldo A. Garcia, Mark Helman, Dan Reznik
We describe four special families of ellipse-inscribed Poncelet triangles about the incircle which maintain certain triangle centers stationary and which also display interesting c…
The stationary focus of the Kiepert parabola over a special Poncelet triangle family
Mark Helman, Ronaldo A. Garcia, Dan Reznik
We show that the focus of the Kiepert in-parabola remains stationary over a family of circle-inscribed Poncelet triangles which contain an equilateral triangle.
Poncelet triangles: conic loci of the orthocenter and of the isogonal conjugate of a fixed point
Ronaldo A. Garcia, Mark Helman, Dan Reznik
We prove that over a Poncelet triangle family interscribed between two nested ellipses , (i) the locus of the orthocenter is not only a conic, but it is…