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.

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