Given the radii of the circles and the points of contact with
the xaxis you can always find the distances DC in terms of the
radii.
The circles will be tangent if and only if the distance AB is
equal to the sum of the radii.
The circles will be separate if and only if the distance AB is
greater than the sum of the radii.
It is possible to prove that the circles given can never
overlap, that is the distance AB is never less than the sum of the
radii.
