The center of an inner Soddy circle. It has equivalent triangle center functions
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the area of the triangle.
Given a point 
not between 
and 
,
a detour of length
 |
(3)
|
is made walking from 
to 
via 
,
the point is of equal detour if the three detours from one side to another via 
are equal. If 
has no angle 
, then the point given by the above trilinear
coordinates is the unique equal detour point. Otherwise, the isoperimetric
point is also equal detour.
