|Information from Kimberling's Encyclopedia of Triangle Centers|
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(a2 + 3b2 - c2)(a2 - b2 + 3c2)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Suppose X is a point, with isogonal conjugate X- 1. It is well known that if the pedal triangle of X is homothetic to the antipedal triangle of X- 1. The Lemoine homothetic center, X(1286), is the homothetic center when X = X(6), and X(3065) is the homothetic center when X = X(2). See also X(1285). (Peter Moses, Dec. 7, 2005)
In general is X = x : y : z (trilinears), then the homothetic center is given by
a(x + y cos C)(x + z cos B) : b(y + z cos A)(y + x cos C): c(z + x cos B)(z + y cos A).This is a correction for trilinears given in TCCT, p. 188.
X(3066) lies on these lines: 2,1350 3,373 6,110 25,182 51,394 107,458 125,381