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  • $\begingroup$ I think that nf in the first block finds the segment whose extended line is closest to a point. But the problem is about distance to a segment only, not to its extended line, isn't it? $\endgroup$ Commented Apr 19, 2013 at 9:01
  • $\begingroup$ How then do you define "distance to a segment"? $\endgroup$ Commented Apr 19, 2013 at 9:02
  • $\begingroup$ Something like Min[EuclideanDistance[p1 + t (p2 - p1), p3]] with 0 < t < 1. $\endgroup$ Commented Apr 19, 2013 at 9:32