The Johnson triangle Δ J_A J_B J_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix [-a b c S_A :c(S^2 + S_A S_C):b(S^2 + S_A S_B) c(S^2 + S_B S_C): - a b c S_B :a(S^2 + S_A S_B) b(S^2 + S_B S_C):a(S^2 + S_A S_C): - a b c S_C], where S, S_A, S_B, and S_C is Conway triangle notation. The Johnson triangle circumcircle is congruent to the Johnson circles and therefore also to the circumcircle of the reference triangle.

Johnson circles | Johnson circumconic | Johnson's theorem | Johnson triangle circumcircle | orthocentric system