Clustering finite size points

I'm looking for a clustering algorithm for a set of points that also have a radius (aka circles). Effectively I have a set of circles each with parameters (x, y, r). Just taking the circle's centre is no good for large circles. For example if I have a small circle close to the edge of a large circle I want them to be in the same cluster.

My current solution is to create a new set of points that spatially sample the circles (i.e. fill the circle with points with some spacing) and use those in an ordinary clustering algorithm, then map back somehow. It feels a bit hacky though.