Another tricky trivia

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*Problem.* Let there be n points on a plane such that with respect to any point, other points lie at different distances from it ( with respect to say $p_1$ if distance$(p_1,p_j)$=distance$(p_1,p_l)$, then $j=l$). For every point, we draw a straight line segment that connects the point to its nearest point. Prove that no two line segments intersect.(except at their endpoints, perhaps)

— 13 Dec 2012 11:28

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