This comes from a GCE O level paper (UCLES) from July 1959.
(It's the second part of a question; the first part provides a hint.)
Students would have solved it using a 'static' approach.
Is a 'dynamic' approach useful here? Probably not for simply solving the task, though it can raise interesting issues and broaden one's understanding.

We look at two dynamic approaches. First, we see what happens when we change the relative size of the circles. On the next page we decrease the size of the circle through C. Can you predict what happens?

a high-res pdf file of this new GEOaa-zz task