The Soddy line cuts the Euler line at the De Longchamps point L. Let Ng be the Nagel point, O the circumcenter, H the orthocenter, N the ninecenter. The Soddy line cuts ONg at T, NNg at U, HNg at V, and we have the ratios
LT : LI : LU : LV = 10 : 15 : 18 : 30    ONg : OT = 3 : 1    NNg : UNg  = 5 : 3    HNg = HV