how to position 12 circles evenly in a big circle

Question

This is a realistic question in my study design needed to be solved. Please help.

In a 3-cm² big circle (area=3-cm², so calculated radius of this big circle=9.77 mm), I need to put 12 small holes (all of same dimension). They should be evenly distributed with 4mm spacing from each other, and should be as close to the edge of the big circle as possible. How to position these small holes and how to calculate radius of the small holes?

Thanks

Answer 1

Here you have three possible solutions based on different packings:

By the way, the optimal packing for 12 circles is this:

Although they are not evenly distributed.

HTH!