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Let G be a circle of radiusR gt 0 . Let...

Let G be a circle of radius`R gt 0` . Let `G_(1),G_(2),"…." ,G_(n)` be n circles of equal radius `r gt 0 ` . Suppose each of the n circles `G_(1),G_(2) "….."G_(n)` touches the circle G externally. Also, for I = 1,2,….,`n-1` , the circle `G_(i)` touches `G_(i+1)` externally , and `G_(n)` touches `G_(1)` externally .Then ,which of the following statements is/are TRUE ?

A

If `n = 4`, then `(sqrt(2)-1) r lt R`

B

If n = 5, then` r lt R `

C

If n = 8, then` (sqrt(2)-1) r lt R`

D

If n = 12, then `sqrt(2) (sqrt(3)+1)r gt R`

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