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Fuhrmann Center


FuhrmannCenter

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann circle).

It is Kimberling center X_(355) (Kimberling 1998, p. 123) and has equivalent triangle center functions

alpha_(355)=acosA-(b+c)cos(B-C)
(1)
alpha_(355)=(a-b+c)cosB+2(b+c)cosBcosC
(2)
alpha_(355)=(2a(b+c)secA+(-a+b+c)(bsecA+csecC))/a.
(3)

See also

Circumcircle Mid-Arc Triangle, Fuhrmann Circle, Fuhrmann Triangle, Mid-Arc Points, Nagel Point, Orthocenter

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Fuhrmann Center

Cite this as:

Weisstein, Eric W. "Fuhrmann Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FuhrmannCenter.html

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