9 points so disposed can be connected with the segments as in the figure without detaching the pencil from the paper and you can't do it with more segments. Can you do the same thing if the points are circles with a diameter "d" > 0 with fewer segments? (For point considering the entity of the fundamental geometry that is devoid of any dimension.). The circles don't overlap.
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d> 0 tells you that circles aren't points. So you can pass also in orher points of the circles that are not the centre( thing that you can't do with points). So you can track segments 3 first from left to right, then from right to left and from left to right again hooked so as to pass through all the circles. Thus, 3 is the correct answer.