as an extend to previous post, we suppose the 2 circles are labeled by subscript 1 and 2.
lets suppose we have the touch point on circle 1, say . thus, the solution of the normal vector of tangent lines are:
where is the right rotation matrix. is the length between 2 touching points.
and the pulse sign for is for the center of the circle is on the right hand size.
the assumed touching point on circle can be expressed by .
sub into the equation, simplify, we have:
again, plus sign for center of circle on left side.