Gergonne Point

$\begin{figure}\begin{center}\BoxedEPSF{GergonnePoint.epsf scaled 900}\end{center}\end{figure}$

The common point of the Concurrent lines from the Tangent points of a Triangle's Incircle to the opposite Vertices. It has Triangle Center Function

$\begin{displaymath} \alpha=[a(b+c-a)]^{-1} = {\textstyle{1\over 2}}\sec^2 A. \end{displaymath}$

It is the Isotomic Conjugate Point of the Nagel Point. The Contact Triangle and Tangential Triangle are perspective from the Gergonne point.

See also Gergonne Line

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.

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. New York: Random House, pp. 11-13, 1967.

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. 22, 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 216, 1929.

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