Question

Let G be a circle of radius R > 0. Let G₁, G₂, ..., G_n be n circles of equal radius r > 0. Suppose each of the n circles G₁, G₂, ..., 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 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 √(√3+1)r > R.

Answer 1

(C) If n = 8, then (√2-1)r < R  /  (D) If n = 12, then √(√3+1)r > R.