Given a triangle and a point not a vertex of , define the -vertex of the circumcevian triangle as the point other than in which the line meets the circumcircle of , and similarly for and . Then is called the circumcevian triangle of (Kimberling 1998, p. 201).
The circumcevian triangle with respect to the point has trilinear vertex matrix
where is the area of and
Circumcevian triangles for various choices of are summarized in the table below.
|circumcircle mid-arc triangle