The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations (t_2 - x_2)·(t_2 - t_1) = 0 (t_1 - x_1)·(t_2 - t_1) = 0 ( left bracketing bar t_1 - x_1 right bracketing bar )^2 = r_1^2 ( left bracketing bar t_2 - x_2 right bracketing bar )^2 = r_2^2. The point of intersection of the two crossing tangents is called the internal similitude center. The point of intersection of the extensions of the other two tangents is called the external similitude center.

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