The Fermat-Steiner Problem

@article{Gueron2002TheFP,
  title={The Fermat-Steiner Problem},
  author={Shay Gueron and Ran Tessler},
  journal={The American Mathematical Monthly},
  year={2002},
  volume={109},
  pages={443 - 451}
}
The original treatment of the problem considered only triangles with acute angles, for which P must be an interior point. Therefore, a discussion of the relative position of P with respect to the triangle did not emerge. Let us first make some simple observations about this relative position: P cannot lie outside ABC because in this case the “nearest point projection”, call it P ′, gives G(P ′) < G(P). By the convexity of the distance function it follows that if P is inside ABC , it is unique… 
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