5 papers · 1 filter
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…
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…
Cramer-Castillon on a Triangle's Incircle and Excircles
Dominique Laurain, Peter Moses, Dan Reznik
The Cramer-Castillon problem (CCP) consists in finding one or more polygons inscribed in a circle such that their sides pass cyclically through a list of points. We study this…