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 , the corresponding Brianchon point is .
The following table gives the Brianchon points for a number of inconics.
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.