The point of concurrence of the joins of the vertices of a triangle and the points of contact of an inconic of the triangle. 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.

heptagon theorem | inconic | Kiepert parabola | Steiner points | Yff parabola

Charles-Julien Brianchon