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 , the corresponding Brianchon point is .

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

inconic	Kimberling	Brianchon point	triangle center function	contact triangle
Brocard inellipse		symmedian point		symmedial triangle
Kiepert parabola		Steiner point		Steiner triangle
Lemoine inellipse		isogonal conjugate of		Lemoine triangle
MacBeath inconic		isotomic conjugate of the circumcenter		MacBeath triangle
Mandart inellipse		Nagel point		extouch triangle
orthic inconic		orthocenter		orthic triangle
Steiner inellipse		triangle centroid		medial triangle
Yff parabola		Yff parabolic point		Yff contact triangle