Let I_A, I_B, and I_C be the vertices of the inner 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 I_A, E_B I_B, and E_C I_C concur at a point known as the second Eppstein point (Kimberling), denoted M by Eppstein. Although Eppstein actually cited, he missed the fact that M is equivalent to the outer Oldknow point defined by Oldknow. The second Eppstein point (originally called the outer Oldknow point) is also the perspectors of a given triangle Δ A B C and the tangential triangles of its inner Soddy Triangle.

first Eppstein point | Soddy circles | Soddy triangles