1. In the plane 5 circles are given such that no three of them have a common point. Can it happen that they have exactly:
a) 12;
b) 24 different intersection points?
Solution
a) Yes, it is possible. It is enough to take 4 circles, each pair of which intersects in two points, and a fifth circle such that it does not intersect the others.
b) No, it is not possible. The first circle can intersect the others in at most 8 points, the second adds at most 6 intersection points, and so on. In total, we have at most different intersection points.
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