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math.MG2025
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…
math.MG2025
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.
math.MG2025
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…