Geodesic
The Ellipse, Monge’s Circle and Other Circles
Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 159-173.

Voir la notice de l'article provenant de la source Heldermann Verlag

New developments of the author's research project on the geometry of conics are presented. For any general point $P$ taken on a given ellipse $H$, some triplets of collinear, peculiar points are described; several angles sharing the same vertex are shown to share the same line as bisector, too. Three new circles linking points belonging to the ellipse $H$, Monge's circle and other conics introduced by the author (the symbiotic ellipse $H_{\Sigma}$ and the circle $\Phi_1$) are described. Unsuspected relationships linking the newly defined objects with a circle previously introduced by the author (denoted \emph{circle $\Omega$}) are described.
Classification : 51M04
Mots-clés : Ellipse, collinear points, angle bisector, concyclic points, symbiotic conics, Monge's circle, bridge-circle 
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     author = {M. Ternullo },
     title = {The {Ellipse,} {Monge{\textquoteright}s} {Circle} and {Other} {Circles}},
     journal = {Journal for geometry and graphics},
     pages = {159--173},
     publisher = {mathdoc},
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M. Ternullo . The Ellipse, Monge’s Circle and Other Circles. Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 159-173. http://geodesic.mathdoc.fr/item/JGG_2020_24_2_JGG_2020_24_2_a1/