The Feuerbach point X_11 (center of the Feuerbach hyperbola) lies on the nine-point circle. The Feuerbach antipode is the antipode of this point on nine-point circle. It has triangle center function α_119 = (-1 + cos B + cos C) csc A[sin(2B) + 2(cos A - 1)(sin B + sin C) + sin(2C)] and is Kimberling center X_119.

Feuerbach hyperbola | Feuerbach point | Jerabek antipode | Kiepert antipode

Karl Wilhelm Feuerbach