The Euler-Gergonne-Soddy triangle is the right triangle Δ Z Fl Ev created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The triangle is always right since the Soddy and Gergonne lines always intersect perpendicularly.) The vertices of this triangle are the de Longchamps point Z (L_S intersection L_E), Fletcher point Fl (L_G intersection L_S), and Evans point Ev (L_G intersection L_E). It is not in perspective with Δ A B C. The circumcircle of the Euler-Gergonne-Soddy triangle is the Euler-Gergonne-Soddy circle.

de Longchamps point | Euler line | Evans point | Fletcher point | Gergonne line | Soddy line