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Characterisations of Kiepert, Jarabek and Feuerbach hyperbolas


Abstract


We obtain several characterisations of the Kiepert, Jarabek, and Feuerbach hyperbolas of a scalene triangle ABC using the family of triangles with vertices on Euler lines of triangles BCP, CAP, and ABP for a variable point P in the plane and the notion of orthologic triangles.

DOI Code: 10.1285/i15900932v18n1p17

Keywords: Orthologic triangles; Feuerbach hyerbola; Kiepert hyperbola; Jarabek hyperbola; Complex numbers

Classification: 51M04

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