Suppose you have a set of circles $\mathcal{C} = {C_1, .., C_n}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius $r$ as the previous circles but with a new centre coordinate.

How can you determine whether the area covered by the $C_{n+1}$ is fully covered by $\mathcal{C}$?

How to do this if the circles can have varying radii?