The excentral triangle, also called the tritangent triangle, of a triangle is the triangle with vertices corresponding to the excenters of .
It is the anticevian triangle with respect to the incenter (Kimberling 1998, p. 157), and also the antipedal triangle with respect to .
The circumcircle of the excentral triangle is the Bevan circle.
Its trilinear vertex matrix is
(1)

The excentral triangle has side lengths
(2)
 
(3)
 
(4)

and area
(5)
 
(6)

where , , and are the area, inradius, and semiperimeter of the original triangle , respectively. It therefore has the same side lengths and area as the hexyl triangle.
The excentral triangle is perspective to every Cevian triangle (Kimberling 1998, p. 157).
The excentralhexyl ellipse passes through the vertex of the excentral and hexyl triangles.
Beginning with an arbitrary triangle , find the excentral triangle . Then find the excentral triangle of that triangle, and so on. Then the resulting triangle approaches an equilateral triangle (Johnson 1929, p. 185; Goldoni 2003). The analogous result also holds for iterative construction of contact triangles (Goldoni 2003).
Given a triangle , draw the excentral triangle and medial triangle . Then the orthocenter of , incenter of , and circumcenter of are collinear with the midpoint of (Honsberger 1995).
The incenter of coincides with the orthocenter of , and the circumcenter of coincides with the ninepoint center of . Furthermore, is the midpoint of the line segment joining the orthocenter and circumcenter of (Honsberger 1995).
The following table gives the centers of the excentral triangle in terms of the centers of the reference triangle for Kimberling centers with .
center of excentral triangle  center of reference triangle  
incenter  incenter of excentral triangle  
triangle centroid  triangle centroid of the excentral triangle  
circumcenter  Bevan point  
orthocenter  incenter  
ninepoint center  circumcenter  
symmedian point  mittenpunkt  
Gergonne point  Gergonne point of excentral triangle  
Nagel point  Nagel point of excentral triangle  
mittenpunkt  mittenpunkt of excentral triangle  
first isodynamic point  third Evans perspector  
second isodynamic point  second Evans perspector  
Clawson point  congruent isoscelizers point  
perspector of abc and orthicoforthic triangle  Ceva conjugate of  
homothetic center of orthic and tangential triangles  isogonal conjugate of  
Euler infinity point  isogonal conjugate of  
second power point  congruent circumcircles isoscelizer point  
third power point  Ceva conjugate of  
perspector of the orthic and intangents triangles  congruent incircles isoscelizer point  
Ceva conjugate of  third isoscelizer point  
crosspoint of and  second isoscelizer point  
triangle centroid of orthic triangle  triangle centroid  
orthocenter of orthic triangle  orthocenter  
symmedian point of orthic triangle  symmedian point  
Kosnita point  Ceva conjugate of  
isogonal conjugate of  equal perimeters isoscelizer point  
isogonal conjugate of  intersection of lines and  
isogonal conjugate of  eigentransform of  
orthocenter of the contact triangle  second midarc point of anticomplementary triangle  
Prasolov point  intersection of lines and  
symmedian point of the anticomplementary triangle  excentral isogonal conjugate of  
isotomic conjugate of incenter  intersection of lines and  
third Brocard point  aleph conjugate of  
Cevapoint of incenter and Clawson point  first isoscelizer point  
Cevapoint of triangle centroid and circumcenter  excentral isogonal conjugate of  
isogonal conjugate of  excentral isogonal conjugate of  
isogonal conjugate of  excentral isogonal conjugate of  
Tarry point  5th Sharygin point 