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.