Two concentric circles have radii
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
and
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
respectively. Determine the greatest possible number of circles that are tangent to both these circles and mutually nonintersecting. Prove that this number lies between
![\frac 32 \cdot \frac{\sqrt R +\sqrt r }{\sqrt R -\sqrt r } -1](/media/m/d/6/6/d6604242c176e5ebda8bda65928d3510.png)
and
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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 $\frac 32 \cdot \frac{\sqrt R +\sqrt r }{\sqrt R -\sqrt r } -1$ and $\frac{63}{20} \cdot \frac{R+r}{R-r}.$