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321. Can three circles have one common point? two common points? three common points? four common points?

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

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Official solution

321. The answers to the first two questions are positive, to the third one - negative. (Provide an explanation.)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.