Optimal Packing of Inscribed Circles on a Circle

[fisico]

Hi, this is the question:

If the area of a circle C is A and there are n circles of radius r that do not overlap, inscribed on C, what is r?

I was thinking of A = n(pi)r^2, or the area of C equals the sum of the areas of the circles with radius r to get r, but since there is space in between the circles that is not occupied by them, (since the circles do not overlap with each other) then that equation must be wrong.

Help please?

Thank you

 

[StatusX]

Are you asking what the largest r could be is? Cause clearly if you make r small enough they will fit. If this is the question, it's a really tough one, and I can't think of a way to approach it. Are you sure this is the question, and what kind of class is it for?

 

[fisico]

if I say that there are 50 circles, n = 50, inscribed in circle C which has area A, and all adjacent circles are touching each other whithout overlaping, then what is their radius?

That's what the question means. (I think)

 

[StatusX]

If you're just allowed to put the circles in any pattern you want, ie, you need to find the arrangement with the tightest packing, this is a very difficult problem. So if this is for a class, make sure you've got the problem right, and let us know what kind of class this is. And if it's just a problem you thought of, as far as I can tell, you won't be able to solve it.