Touching Circles

These circles do not touch externally, that cannot be proven.
C1: has a center at (-1, -1) and a radius of 5
C2: has a center at (7, 1) and a radius of 3

if k is a third circle where C1 and C2 touch internally, the formula would be:

(x-2.0295)^2 + (y+0.2425)^2 = (8.12)^2

Do you understand how yoyoman did all this or do you need some explanation?

If the circles just touched then the distance between their centres would be exactly equal to the sum of their radii.

This is not the case, can you tell me (with explanation) if they overlap or if they don't touch at all?