The circum-orthic triangle is the circumcevian triangle of a triangle with respect to the orthocenter (Kimberling 1998, p. 163). The circum-orthic triangle of a triangle is also the image of the orthic triangle in the homothecy centered at the orthocenter of and having similitude ratio 2.

It has trilinear vertex matrix

where , , and .

Its area is

where is the area of .

The following table gives the centers of the circum-orthic triangle in terms of the centers of the reference triangle corresponding to Kimberling centers .

center of circum-orthic triangle | center of reference triangle | ||

circumcenter | circumcenter | ||

anticomplement of | |||

Tarry point | Collings transform of | ||

Steiner point | Collings transform of | ||

focus of Kiepert parabola | Gibert point | ||

triangle centroid of the antipedal triangle of | triangle centroid of dual triangle of | ||

isogonal conjugate of | Napoleon crossdifference |