Hi Felix.

You pose an interesting question.

On google, found a way to construct the two centers of similitude, (There are 0, 1, or 2 such centers, depending) for
two circles, by copying the red line to the green line, and making construction lines.

http://www.cut-the-knot.org/Curriculum/Geometry/TangentTwoCirclesII.shtml

http://en.wikipedia.org/wiki/Homothetic_center





( The inner tangent line just happens to be close to the points where the red and green lines intersect the circle.)