Perhaps a rather elementary question, but I simply couldn't figure out the calculations on this one. Say one takes a circle centered at the origin with radius $R$. He or she then proceeds to place $N$ circles with radius $r$ ($R > r$) on the larger circles circumference equidistantly, so every $2 \pi / N$ in the angular sense. What is then the relationship between $R$ and $r$ such that all neighboring circles exactly touch?
I've been trying to write down some equations with arc lengths and such for $N = 4$, but I can't seem to get anything sensible out of it.