Feuerbach Point

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

$$\alpha=1-\cos(B-C).$$

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.