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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 H and the Nagel point N.

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

$R\sqrt{\frac{a^3-a^{2}b-a{b}^2+b^3-a^{2}c+3abc-b^{2}c-a{c}^2+c^3}{abc}},$

which is also the distance between the circumcenter and incenter.

See also

• Nagel point
• Incircle and excircles of a triangle

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.