Geodesic
Singular Fregier Conics in Non-Euclidean Geometry
Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 201-208
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The hypotenuses of all right triangles inscribed into a fixed conic C with fixed right-angle vertex p are incident with the Frégier point f to p and C. As p varies on the conic, the locus of the Frégier point is, in general, a conic as well. We study conics C whose Frégier locus is singular in Euclidean, elliptic and hyperbolic geometry. The richest variety of conics with this property is obtained in hyperbolic plane while in elliptic geometry only three families of conics have a singular Frégier locus.
Classification : 51M04, 51M09, 51N35
Mots-clés : Fregier point, Fregier conic, Thales' theorem, hyperbolic geometry, elliptic geometry, singular conic 
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     author = {H.-P. Schroecker},
     title = {Singular {Fregier} {Conics} in {Non-Euclidean} {Geometry}},
     journal = {Journal for geometry and graphics},
     pages = {201--208},
     year = {2017},
     volume = {21},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a5/}
}
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H.-P. Schroecker. Singular Fregier Conics in Non-Euclidean Geometry. Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a5/