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Feuerbach Point

\begin{figure}\begin{center}\BoxedEPSF{feuerbach_point.epsf scaled 800}\end{center}\end{figure}

The point $F$ at which the Incircle and Nine-Point Circle are tangent. It has Triangle Center Function

\begin{displaymath}
\alpha=1-\cos(B-C).
\end{displaymath}

See also Feuerbach's Theorem


References

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 200, 1929.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Salmon, G. Conic Sections, 6th ed. New York: Chelsea, p. 127, 1954.




© 1996-9 Eric W. Weisstein
1999-05-26