Brianchon Point

The point of concurrence of the joins of the vertices of a triangle and the points of contact of an inconic of the triangle (Veblen and Young 1938, p. 111; Eddy and Fritsch 1994). The Brianchon point of an inconic is often called the perspector of the inconic because it is the perspector of the reference triangle and the triangle of the points of contact.

For inconic parameters x:y:z, the corresponding Brianchon point is 1/x:1/y:1/z.

The following table gives the Brianchon points for a number of inconics.

See also

Heptagon Theorem, Inconic, Kiepert Parabola, Steiner Points, Yff Parabola

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Eddy, R. H. and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle." Math. Mag. 67, 188-205, 1994.Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "The Heptagon Theorem." §2.1 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 8-11, 1974.Veblen, O. and Young, J. W. Projective Geometry, 2 vols. Boston, MA: Ginn, 1938.

Referenced on Wolfram|Alpha

Brianchon Point

Cite this as:

Weisstein, Eric W. "Brianchon Point." From MathWorld--A Wolfram Web Resource.

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