insimilicenter | internal center of similitude

In general, the internal similitude center of two circles C_1 = C(x_1, r_1) and C_2 = C(x_2, r_2) with centers given in Cartesian coordinates is given by Si(C_1, C_2) = (r_1 x_2 + r_2 x_1)/(r_1 + r_2). In trilinear coordinates, the internal center of similitude is given by α:β:γ, where α | = | (a r_1(a α_1 + b β_1 + c γ_1) α_2 + a r_2(a α_2 + b β_2 + c γ_2) α_1)/a β | = | (b r_1(a α_1 + b β_1 + c γ_1) β_2 + b r_2(a α_2 + b β_2 + c γ_2) β_1)/b γ | = | (c r_1(a α_1 + b β_1 + c γ_1) γ_2 + c r_2(a α_2 + b β_2 + c γ_2) γ_1)/c.

external similitude center | homothetic center | midcircle | similitude center