The two circles are disjoint.
The result is two tangent circles with one so large it approachers being a line.
Let's look at the locus of the centers of the tangent circles as the point of tangency moves along the larger circle.
Notice in this case, the locus is two hyperbola, still with the centers of the original circles as the foci.
Click here to open a GSP sketch to the the animation of the point, drawing the two hyperbola.
It is interesting to see, and easier to view the two hyperbola as the result of the envelope of the tangent lines.
Click here to see that animation in a GSP sketch.
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