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
![[csc(1/3(C-B)) csc(1/3(B+2C)) -csc(1/3(C+2B)); -csc(1/3(A+2C)) csc(1/3(A-C)) csc(1/3(C+2A)); csc(1/3(A+2B)) -csc(1/3(B+2A)) csc(1/3(B-A))].](/images/equations/CircumtangentialTriangle/NumberedEquation1.svg) |
All triangle centers of the circumtangential triangle correspond to the circumcenter of the reference triangle.
