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)
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(2)
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and their centers are
(3)
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(4)
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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.