
Journal for Geometry and Graphics 21 (2017), No. 2, 201208 Copyright Heldermann Verlag 2017 Singular Fregier Conics in NonEuclidean Geometry HansPeter Schroecker Faculty of Engineering Sciences, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria hanspeter.schroecker@uibk.ac.at The hypotenuses of all right triangles inscribed into a fixed conic C with fixed rightangle 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. Keywords: Fregier point, Fregier conic, Thales' theorem, hyperbolic geometry, elliptic geometry, singular conic. MSC: 51M04; 51M09, 51N35 [ Fulltextpdf (144 KB)] for subscribers only. 