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Journal for Geometry and Graphics 24 (2020), No. 2, 159--173
Copyright Heldermann Verlag 2020



The Ellipse, Monges Circle and Other Circles

Maurizio Ternullo
INAF - Osservatorio Astrofisico di Catania, Catania, Italy
mternullo@oact.inaf.it



[Abstract-pdf]

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.

Keywords: Ellipse, collinear points, angle bisector, concyclic points, symbiotic conics, Monge's circle, bridge-circle.

MSC: 51M04

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