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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.

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    $\begingroup$ If you're assuming the first truth, and if four could fit into a half circle, how much would fit in a whole circle? $\endgroup$ – David Peterson Sep 26 '14 at 22:37
  • $\begingroup$ @David Peterson, Thank you for your comment. I was thinking of a proof only involving "fundamental" geometrical facts, i.e., a self-contained proof $\endgroup$ – John P Sep 26 '14 at 22:39
  • $\begingroup$ Perhaps I am misunderstanding "interior" but to me it is not a well known fact that $6$ interior disjoint circles of radius $1/2$ can be centered in a circle of radius $1$. See en.wikipedia.org/wiki/Circle_packing_in_a_circle $\endgroup$ – Henry Sep 26 '14 at 22:45
  • $\begingroup$ @Henry Sorry for the confusion. 6 interior disjoint circles of radius 1/2 can not be centered in a circle of radius 1, but can if not restricted to the interior. I am on the otherhand indeed interested in the restriction of halfcircle and interior. The 6 circle part was just to provide some context. $\endgroup$ – John P Sep 26 '14 at 22:47
  • $\begingroup$ What makes a circle "interior"? Does the circle have to be entirely in the bigger circle, or just its centre with part of the smaller circle being outside the bigger circle? $\endgroup$ – Henry Sep 26 '14 at 22:49

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