The triangle formed by the points of pairwise intersection of the three intangents. It is not in perspective with .
It has trilinear vertex matrix
(1)

or
(2)

(Kimberling 1998, p. 161).
It has side lengths
(3)
 
(4)
 
(5)

where is the inradius of the reference triangle, is its semiperimeter, and is its circumradius. It has area
(6)
 
(7)

where is the area of .
The intangents circle is the circumcircle of the intangents triangle.