Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines E_A J_A, E_B J_B, and E_C J_C concur at a point known as the first Eppstein point E p_1 (Kimberling), denoted M' by Eppstein. Although Eppstein actually cited, he missed the fact that M' is equivalent to the inner Oldknow point defined by Oldknow. The first Eppstein point (originally called the inner Oldknow point) is also the perspectors of a given triangle Δ A B C and the tangential triangles of its outer Soddy triangle.

second Eppstein point | Soddy circles | Soddy triangles