# Deploying circles on 2D space to cover most of points

My question is related to this one

Minimize number of circles to cover set of points

In a 2D space, I have a set of points. I can deploy up to $$k$$ circles with radius $$r$$ to the space, and my goal is to maximize the number of points that will be put inside these circles. There are two cases: a) Either the circles cannot overlap b) Or they can.

I am completely stuck here. I appreciate your help.

For every point $$v$$, start by drawing a circle with radius $$r$$ such that $$v$$ is at its center.
Now, observe the following nice property: Let $$d$$ be a point in space such that it is contained in $$m$$ of the drawn circles. Then, placing a circle with radius $$r$$ with its middle at $$d$$ would cover those $$m$$ points.
Hence, your algorithm should start by "drawing" the $$n$$ circles, and applying an algorithm to find all intersections between the drawn triangles and to get the number of intersections in them.