Intersection of the black circle with centre (-1,-1), radius 1 and of the green circle with centre (-2,0), radius 3:

there is no intersection; the centers are √2 apart.

Intersection of the black circle with centre (1,1), radius 1 and of the violet circle with centre (-2,0), radius 2:

the points (-1.41...,-1.91...) and (-0.0885...,-0.5885...); the centers are √2 apart.

Intersection of the red circle with centre (-4,2.5), radius 1 and of the violet circle with centre (-2,0), radius 2:

there is no intersection; the centers are √10.25 apart.

If the distance C1C2 is > R1+R2 there is no intersection.