info prev up next book cdrom email home

Fuhrmann Triangle

\begin{figure}\begin{center}\BoxedEPSF{FuhrmannTriangle.epsf scaled 1000}\end{center}\end{figure}

The Fuhrmann triangle of a Triangle $\Delta ABC$ is the Triangle $\Delta F_CF_BF_A$ formed by reflecting the Mid-Arc Points $M_{AB}$, $M_{AC}$, $M_{BC}$ about the lines $AB$, $AC$, and $BC$. The Circumcircle of the Fuhrmann triangle is called the Fuhrmann Circle, and the lines $F_AM_{BC}$, $F_BM_{AC}$, and $F_CM_{AB}$ Concur at the Circumcenter $O$.

See also Fuhrmann Circle, Mid-Arc Points


Fuhrmann, W. Synthetische Beweise Planimetrischer Sätze. Berlin, p. 107, 1890.

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 228-229, 1929.

© 1996-9 Eric W. Weisstein