It is a well known fact that at most 7 interior disjoint circles of radius 1/2 can be centered in a circle of radius 1; note that they don't need to be fully contained in the radius 1 circle.
I am interested in a simple proof idea to show that at most 3 interior disjoint circles of radius 1/2 can be centered in the interior of a halfcircle of radius 1.
While intuitively clear, I am lacking an idea as how to approach the proof and would appreciate any pointers.