Answer:
If d<2, there is no intersection
If d=2, there is one intersection
If 2<d<8, there are two intersections
If d=8, there is one intersection
if d>8, there is no intersection
Step-by-step explanation:
If d<2 (the difference between both radius is 2), the little circle is inside the big one. Thus there is no intersection.
If d=2, the little circle is inside but tangent to the big one. There is one intersection then.
If 2<d<8, there are two intersections since the little circle has a portion outside the big one, and another portion inside.
If d=8, the little circle is tangent to the big one from outside. There is one intersection then.
if d>8, the little circle is completely exterior to the big one. Thus, there is no intersection.
Please find attached the figure for d = 10. The big circle is centered and the other is offset by 10.
