Let G be a circle of radius $\mathrm{R}>0$. Let $\mathrm{G}_1, \mathrm{G}_{2 e a v e} \mathrm{G}_2$ be n circles of equal radius $\mathrm{r}>0$. Suppose each of the $n$ circles $G_1 G_{20000} G_2$ touches the circle $G$ externally. Also, for $i=1,2$ roaws $n-1$, the circle $G_i$ touches $G_{i+1}$ externally, and $G_{\lambda z}$ touches $G_1$ externally. Then, which of the following statements is/are TRUE?
Select ALL correct options:
A
If $\mathrm{n}=4$, then $(\sqrt{2}-1) \mathrm{r}<\mathrm{R}$
B
If $\mathrm{n}=5$, then $\mathrm{r}<\mathrm{R}$
C
If $\mathrm{n}=8$, then $(\sqrt{2}-1) \mathrm{r}<\mathrm{R}$
D
If $\mathrm{n}=12$, then $\sqrt{2}(\sqrt{3}+1) \mathrm{r}>\mathrm{R}$
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