Maximum non-intersecting subset of circles

Question

We are given a set of circles, stored by their center points in an array $A$. In particular, the center of the $i$th circle is at coordinates $(A[i].x, A[i].y)$. All the circles have radius of $k$.

I want to find a subset of circles such that no circles in this subset intersect with each other, such that this subset is as large as possible.

I'm asked to find a way to solve this using a backtracking algorithm. Rather than to do it with brute force, is there a effective way to prune some of the branches?