Let G be a circle of radius R > 0. Let G1, G2, …, Gn be n circles of equal radius r > 0. Suppose each of the n circles G1, G2, …, Gn touches the circle G externally. Also, for i = 1, 2, …, n − 1, the circle Gi touches Gi+1 externally, and Gn touches G1 externally. Then, which of the following statements is/are TRUE ?
1
If n = 4, then (√2 - 1) r < R
2
If n = 5, then r < R
3
If n = 8, then (√2 - 1) r < R
4
If n = 12, then √2(√3 + 1) r > R