Planar configuration of straight connecting lines

[Radu Grigore told me this problem. I think may have heard it 20 years earlier from Jan van de Snepscheut.]

Given an even number of points in general positions on the plane (that is, no three points co-linear), can you partition the points into pairs and connect the two points of each pair with a single straight line such that the straight lines do not overlap?

September 2011

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