SOLVE VIA MATHEMATICAL INDUCTION

2. There are n circles in a plane. Prove that the regions in the plane divided by the circles can be colored with two colors in such a way that no two regions sharing some length of border are the same color. Each new circle should overlap at least one previous circle. For example, upon adding a sixth circle, you might have the following image: 2. There are n circles in a plane. Prove that the regions in the plane divided by the circles can be colored with two colors in such a way that no two regions sharing some length of border are the same color. Each new circle should overlap at least one previous circle. For example, upon adding a sixth circle, you might have the following image