Problem
Let G be a circle of radius R > 0. Let G1, G2, …, Gn be n circles of equal radius r > 0. Suppose each of 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?
A If n = 4, then (√2 − 1)r < R
B If n = 5, then r < R
C If n = 8, then (√2 − 1)r < R
D If n = 12, then (√2(√3 + 1))r > R