Abstract. We obtain several characterizations of the Kiepert, Jarabek, and Feuerbach hyperbolas of a tringle ABC using the antipedal tringles of a variable point P in the plane and the notion of orthologic tringles. Our arguments are algebraic and use complex numbers.
1991 Mathematics Subject Classification. 14Q05, 53A04, 14H45, 51N20.
Key words and phrases. Feuerbach, Kiepert, Jarabek, hyperbola, orthology, antipedal tringle, complex numbers, homothetic.