The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise in a single point. Denoting the radius ρ, the exact trilinear coordinates of the centers of the A-, B-, and C-circles are given by O_A | = | (2Δ - (b + c) ρ)/a :ρ:ρ O_B | = | ρ:(2Δ - (a + c) ρ)/b :ρ O_C | = | ρ:ρ:(2Δ - (a + b) ρ)/c.

Johnson's theorem | Johnson-Yff circles