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# Feuerbach Hyperbola

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are given by

meaning it has trilinear equation

(Kimberling 1998, p. 237).

Its center is the Feuerbach point (Kimberling 1998, p. 237).

It passes through the vertices of a triangle and Kimberling centers for (incenter),

4 (orthocenter), 7 (Gergonne point), 8 (Nagel point), 9 (mittenpunkt), 21 (Schiffler point), 79, 80, 84, 90, 104, 177, 256, 294, 314, 885, 941, 943, 981, 983, 987, 989, 1000, 1039, 1041, 1061, 1063, 1156, 1172, 1251, 1320, 1389, 1392, 1476, 1896, 1937, 2298, 2320, 2335, 2344, 2346, 2481, 2648, and 2997.

The Feuerbach hyperbola is the isogonal conjugate of the line , where is the circumcenter and is the incenter of .

Circumconic, Feuerbach's Conic Theorem, Kiepert Hyperbola, Jerabek Hyperbola, Stammler Hyperbola

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## References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Mandart H. "Sur l'hyperbole de Feuerbach." Mathesis, 81-89, 1893.Rigby, J. F. "A Concentrated Dose of Old-Fashioned Geometry." Math. Gaz. 57, 296-298, 1953.

## Referenced on Wolfram|Alpha

Feuerbach Hyperbola

## Cite this as:

Weisstein, Eric W. "Feuerbach Hyperbola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FeuerbachHyperbola.html