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
a
3
−
a
2
b
−
a
b
2
+
b
3
−
a
2
c
+
3
a
b
c
−
b
2
c
−
a
c
2
+
c
3
a
b
c
,
which is also the distance between the circumcenter and incenter.