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 ρ_1 | = | (r R)/(R + r) ρ_2 | = | (r R)/(R - r), and their centers are α_1478 | = | 1 + 2cos B cos C α_1479 | = | 1 - 2cos B cos C, which are Kimberling centers X_1478 and X_1479, respectively.

Johnson circles | Johnson's theorem | orthocentric system | Yff circles