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+cosA cosA-cosC cosA-cosB; cosB-cosC 1+cosB cosB-cosA; cosC-cosB cosC-cosA 1+cosC],](/images/equations/IntangentsTriangle/NumberedEquation1.svg) |
(1)
|
or
![[a(b+c-a) (c-a)(c+a-b) (b-a)(b+a-c); (c-b)(c+b-a) b(c+a-b) (a-b)(a+b-c); (b-c)(b+c-a) (a-c)(a+c-b) c(a+b-c)]](/images/equations/IntangentsTriangle/NumberedEquation2.svg) |
(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.
