Question 38
(ROM) Two concentric circles have radii $R$ and $r$ respectively. Determine the greatest possible number of circles that are tangent to both these circles and mutually nonintersecting. Prove that this number lies between $\frac32\cdot\frac{\sqrt R+\sqrt r}{\sqrt R-\sqrt r}-1$ and $\frac{63}{20}\cdot\frac{R+r}{R-r}$.