Geodesic
Common Tangents to Ellipse and Circles, the 13-Point Circle and Other Theorems
Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 45-63 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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.
Classification : 51M04, 51N20
Mots-clés : ellipse, harmonic range, collinear points, concyclic points, symbiotic ellipse, Monge's circle, circle inversion 
@article{JGG_2019_23_1_JGG_2019_23_1_a5,
     author = {M. Ternullo },
     title = {Common {Tangents} to {Ellipse} and {Circles,} the {13-Point} {Circle} and {Other} {Theorems}},
     journal = {Journal for geometry and graphics},
     pages = {45--63},
     year = {2019},
     volume = {23},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a5/}
}
TY  - JOUR
AU  - M. Ternullo 
TI  - Common Tangents to Ellipse and Circles, the 13-Point Circle and Other Theorems
JO  - Journal for geometry and graphics
PY  - 2019
SP  - 45
EP  - 63
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a5/
ID  - JGG_2019_23_1_JGG_2019_23_1_a5
ER  - 
%0 Journal Article
%A M. Ternullo 
%T Common Tangents to Ellipse and Circles, the 13-Point Circle and Other Theorems
%J Journal for geometry and graphics
%D 2019
%P 45-63
%V 23
%N 1
%U http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a5/
%F JGG_2019_23_1_JGG_2019_23_1_a5
M. Ternullo . Common Tangents to Ellipse and Circles, the 13-Point Circle and Other Theorems. Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 45-63. http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a5/