## Harmonic Conjugate Points

Given Collinear points , , , and , and are harmonic conjugates with respect to and if

The distances between such points are said to be in Harmonic Ratio, and the Line Segment depicted above is called a Harmonic Segment.

Harmonic conjugate points are also defined for a Triangle. If and have Trilinear Coordinates and , then the Trilinear Coordinates of the harmonic conjugates are

(Kimberling 1994).

References

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

Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 13-14, 1990.

Phillips, A. W. and Fisher, I. Elements of Geometry. New York: American Book Co., 1896.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. New York: Viking Penguin, p. 92, 1992.