Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to the original three and passing through the points of pairwise intersection. These circles have radii
 |  |  |
(1)
|
 |  |  |
(2)
|
and their centers are
 |  |  |
(3)
|
 |  |  |
(4)
|
which are Kimberling centers 
and 
, respectively.
The circle functions of the Johnson circles do not correspond to any Kimberling centers, and the Johnson-Yff circles do not pass through any Kimberling centers.
The sets of points (
, 
, 
, 
) and (
, 
, 
, 
) comprise two orthocentric
systems.
