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Fuhrmann circle

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Fuhrmann circle

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.

References

Fuhrmann circle Wikipedia


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