How many circles with radius $r_1$ can be inscribed in circle with radius $r_2$

Question

Is there formula for finding the number of inscribed circles in a bigger circle?

For example: Little circles radius: $7 cm$; Big circle radius: $50cm$;

Answer 1

I think what you are looking for is this:

The big circle radius is $r_2=AB$ and the little circle radius $r_1=CB=CE$. Recognizing the right triangle $AEC$ you find the relationship

$$ \sin \frac{\alpha}{2} = \frac{CE}{AC} = \frac{r_1}{r_2-r_1} $$

once you have the angle $\alpha$ you can calculate the number of circles that fit in $2\pi$ as $$N={\rm integer}(\frac{2\pi}{\alpha})$$