The circumtangential triangle is an equilateral triangle formed by the three points on the circumcircle of a reference triangle at which the line , where is the isogonal conjugate, is tangent to the circumcircle (Kimberling 1998, p. 166).
Note that it is not in perspective with .
It has trilinear vertex matrix
All triangle centers of the circumtangential triangle correspond to the circumcenter of the reference triangle.