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I don’t entirely get the reason for the +1 in the regions equation

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Great question! The + 1 is to indicate that the circle always has one region when we start off (the circle itself). Or you can also look at when you have no lines and see that you still have one region which is just the circle itself. Hope that makes sense!

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So we are considering: the case lines intersect, the case where they don’t and the case where there are no lines

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You are exactly right!

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Thanks a lot!

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