A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points.
The limiting points correspond to the point circles of a coaxal system, and the limiting points of a coaxal system are inverse points with respect to any circle of the system.
To find the limiting point of two circles of radii 
and 
with centers separated by a distance 
, set up a coordinate system centered on the circle of radius
and with the other circle centered at
. Then the equation for the position
of the center of the inverted circles with inversion center 
,
 |
(1)
|
becomes
 |  |  |
(2)
|
 |  |  |
(3)
|
for the first and second circles, respectively. Setting 
gives
 |
(4)
|
and solving using the quadratic equation gives the positions of the limiting points as
 |
(5)
|
