What if the inner circle could be a different size to the outer circles?
When you alter the size of the inner circle, the equilateral triangle becomes an isosceles triangle at the center of the inner circle. The angle at the inner circle depends on the distance between the center of the inner circle and the center of the outer circles. The smaller the distance, the more obtuse the angle, thus less circles fit around. A greater distance due to a larger center circle makes for a more acute angle and thus more circles can fit around the center circle. I'm not sure if what I just said is very clear, but that would be my reasoning of what happens when you change the size of the inner circle. Not a very mathematical explanation, but it makes sense to me.
Nice article, I'll be waiting for part 2