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four points in a plane

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Two line segments in the plane 2011-08-15
From Tim:
For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.

Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value. Prove that these segments have no common points.

Answered by Chris Fisher.
 
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