4 papers
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…
Stable umbilical points of a W-congruence
Marcos Craizer, Ronaldo Alves Garcia
The class of -congruences is a central object of Projective Differential Geometry. Nevertheless, their singularities has not been extensively studied. In this paper we prove a c…