Also, if you are only using circles (maybe could be expanded to more general cases somehow) and need a very precise circle collision, a simple distance comparison could actually do the job I would say:
a circle of center A and radius 100, and a circle of center B and radius 10:
They are overlapping if the distances between them is lower or equal than the sum of the two radiuses.
But I think this could be more demanding at the end (maybe not), so maybe not a great idea on my part.