The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle.
Its trilinear vertex matrix is
The following table gives the centers of the circumcircle mid-arc triangle in terms of the centers of the reference triangle for Kimberling centers with .
center of circumcircle mid-arc triangle | center of reference triangle | ||
circumcenter | circumcenter | ||
orthocenter | incenter | ||
nine-point center | midpoint of incenter and circumcenter | ||
symmedian point | midpoint of and | ||
de Longchamps point | Bevan point | ||
perspector of abc and orthic-of-orthic triangle | external similitude center of circumcircle and incircle | ||
homothetic center of orthic and tangential triangles | midpoint of and | ||
Euler infinity point | isogonal conjugate of | ||
triangle centroid of orthic triangle | midpoint of and | ||
orthocenter of orthic triangle | midpoint of and | ||
symmedian point of orthic triangle | midpoint of incenter and symmedian point | ||
Kosnita point | Schiffler point | ||
isogonal conjugate of | -Ceva conjugate of | ||
anticomplement of Feuerbach point | |||
isogonal conjugate of | -isoconjugate of | ||
Tarry point | psi(incenter, symmedian point) | ||
Steiner point | antipode of |