Let be the point at which the -Excircle meets the side of a Triangle , and define and similarly. Then the lines , , and Concur in the Nagel Point.

The Nagel point can also be constructed by letting be the point half way around the Perimeter of
starting at , and and similarly defined. Then the lines , , and concur in the Nagel point.
It is therefore sometimes known as the Bisected Perimeter Point (Bennett *et al. *1988, Chen *et al. *1992, Kimberling 1994).

The Nagel point has Triangle Center Function

It is the Isotomic Conjugate Point of the Gergonne Point.

**References**

Altshiller-Court, N. *College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed.*
New York: Barnes and Noble, pp. 160-164, 1952.

Bennett, G.; Glenn, J.; Kimberling, C.; and Cohen, J. M. ``Problem E 3155 and Solution.'' *Amer. Math. Monthly* **95**, 874, 1988.

Chen, J.; Lo, C.-H.; and Lossers, O. P. ``Problem E 3397 and Solution.'' *Amer. Math. Monthly* **99**, 70-71, 1992.

Eves, H. W. *A Survey of Geometry, rev. ed.* Boston, MA: Allyn and Bacon, p. 83, 1972.

Gallatly, W. *The Modern Geometry of the Triangle, 2nd ed.* London: Hodgson, p. 20, 1913.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, pp. 184 and 225-226, 1929.

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

Kimberling, C. ``Nagel Point.'' http://cedar.evansville.edu/~ck6/tcenters/class/nagel.html.

© 1996-9

1999-05-25