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JEE Advanced 2022 Paper 2

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Question : 12

Total: 54

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?

If n=4, then (√2−1)r<R
If n=5, then r<R
If n=8, then (√2−1)r<R
If n=12, then √2(√3+1)r>R

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