The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference
triangle 
obtained by rotating the circumtangential
triangle by 
radius about its circumcenter (Kimberling 1998, pp. 166-167). Note that it is
not in perspective with 
.
It has trilinear vertex matrix
![[sec(1/3(C-B)) -sec(1/3(B+2C)) -sec(1/3(C+2B)); -sec(1/3(A+2C)) sec(1/3(A-C)) -sec(1/3(C+2A)); -sec(1/3(A+2B)) -sec(1/3(B+2A)) sec(1/3(B-A))].](/images/equations/CircumnormalTriangle/NumberedEquation1.svg) |
All triangle centers of the circumnormal triangle correspond to the circumcenter of the reference triangle.
