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Journal for Geometry and Graphics 23 (2019), No. 1, 045--063
Copyright Heldermann Verlag 2019

Common Tangents to Ellipse and Circles, the 13-Point Circle and Other Theorems

Maurizio Ternullo
INAF -- Osservatorio Astrofisico, v. S. Sofia 78, 95125 Catania, Italy

New developments of the author's research project on the geometry of conics are presented. Special attention is paid to the relationships among the ellipse and three circles, previously introduced by the author and belonging to the elliptic and hyperbolic pencil of circles defined by the ellipse foci. Among the newly defined points, arising as intersections of the geometrical objects under examination, eight triplets of collinear points and as many quadruplets of concyclic points are recognized. Eight new special points are shown to be concyclic on the well known circle through P and the ellipse foci.

Keywords: ellipse, harmonic range, collinear points, concyclic points, symbiotic ellipse, Monge's circle, circle inversion.

MSC: 51M04; 51N20

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