Fermat Point of a Triangle

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  1. Move P to shorten TotalNetwork=AP+BP+CP (.ggb)
     
  2. Adjust P to shorten TotalNetwork. Note: minimization appears to occur when all angles are 120 degrees (.ggb)
     
  3. Construction of the Fermat Point of triangle ABC (all angles < 120 degrees) (.ggb)
     
  4. Proof that Fermat Point minimizes AP+BP+CP (all angles < 120 degrees) (.ggb)
     
  5. Exploring the case when an angle exceeds 120 degrees (.ggb)