In geometry, the Fuhrmann circle of a triangle, named after the German Wilhelm Fuhrmann (1833–1904), is the circle that has as a diameter the line segment between the orthocenter and the Nagel point. This circle is identical with the circumcircle of the Fuhrmann triangle.

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

which is also the distance between the circumcenter and incenter.

denotes the radius of the triangles incircle.

Notes

Further reading

• Nguyen Thanh Dung: "The Feuerbach Point and the Fuhrmann Triangle". Forum Geometricorum, Volume 16 (2016), pp. 299–311.

• J. A. Scott: An Eight-Point Circle. In: The Mathematical Gazette, Volume 86, No. 506 (Jul., 2002), pp. 326–328 (JSTOR)

External links

• Fuhrmann circle