In general, the external 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 Se(C_1, C_2) = (r_1 x_2 - r_2 x_1)/(r_2 - r_1). In trilinear coordinates, the external 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.
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