Fuhrmann circle

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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

R\sqrt{\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.[1]

[edit] See also

[edit] Notes

  1. ^ Eric W. Weisstein, Fuhrmann Circle at MathWorld.