Computing convex hull of a bunch of circles

Question

I am stuck on the following question

Let S be a set of n (possibly intersecting) unit circles in the plane.
Design a O(nlog(n)) algorithm to compute the convex hull of S and
returns an array in which stores the coordinates of the centers
of the units disks that are on the border of the convex hull.

No circles will be the same and no three circles will be colinear.

This is the last question and the only one I don't know how to tackle. I understand convex hull algorithms such as the gift-wrapping one.

Any pointers in the right direction would be really appreciated.

Thanks a ton in advance.

Answer 1

Just compute the convex hull of the centers.
Since all the circles ('disks' would have been a better and equivalent formulation) have the same radius, the convex hull of the circles is the Minkowski sum of
{the convex hull of the centers} and {the unit disk}.