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Solving idea for problem 2: in this problem we consider a circle as the area bounded by its circumference and not only its circumference. This implies, for instance, that the algorithm considers two circles intersect when one of them is completely contained within the other (even if their circumferences don’t touch in any point).
Geometrically the intersection condition for two circles (to have common points – either on the circumference or inner) can be formulated like: if the distance between their centers falls in the closed interval [|R1-R2|, R1+R2], then the two circles intersect....

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