Fuhrmann circle

Fuhrmann circle

In geometry, the Fuhrmann circle of a triangle is the circle with a diameter of the line segment between the orthocenter and the Nagel point.

The radius of the Fuhrmann circle of a triangle with sides "a", "b", and "c" and circumradius "R" is

: Rsqrt{frac{a^3-a^2b-ab^2+b^3-a^2c+3abc-b^2c-ac^2+c^3}{abc,

which is also the distance between the circumcenter and incenter. [mathworld|urlname=FuhrmannCircle|title=Fuhrmann Circle]

ee also

*Nagel point
*Incircle and excircles of a triangle

Notes


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