The triangle 
that is externally tangent to the excircles
and forms their triangular hull is called the extangents triangle (Kimberling 1998,
p. 162). It is homothetic to the orthic
triangle, and the homothetic center is known
as the Clawson point.
The extangents triangle has trilinear vertex matrix
![[-(x+1) x+z x+y; y+z -(y+1) y+x; z+y z+x -(z+1)],](/images/equations/ExtangentsTriangle/NumberedEquation1.svg) |
(1)
|
where 
,
,
,
or equivalently,
![[-a/((a+b-c)(a-b+c)) (a+c)/((a-b+c)(a+b+c)) (a+b)/((a+b-c)(a+b+c)); (b+c)/((-a+b+c)(a+b+c)) -b/((a+b-c)(-a+b+c)) (a+b)/((a+b-c)(a+b+c)); (b+c)/((-a+b+c)(a+b+c)) (a+c)/((a-b+c)(a+b+c)) -c/((-a+b+c)(a-b+c))].](/images/equations/ExtangentsTriangle/NumberedEquation2.svg) |
(2)
|
It has area
![Delta^'=([(a^3+b^3+c^3)-(a+b)(b+c)(c+a)]^2secAsecBsecC)/(8a^2b^2c^2)Delta,](/images/equations/ExtangentsTriangle/NumberedEquation3.svg) |
(3)
|
where 
is the area of 
.
The circumcircle of the extangents triangle is the extangents circle.
Its incenter 
coincides with the circumcenter 
of triangle 
, where 
are the excenters of 
. The inradius 
of the incircle of 
is
 |
(4)
|
where 
is the circumradius of 
, 
is the inradius, and 
are the exradii (Johnson 1929,
p. 192).
