File:Fermat Point.svg - Wikipedia

Description Constructing the Fermat Point of a given triangle: Draw three regular triangles on each side of it, join their outlying vertex with the opposite triangle's vertex, and the lines intersect at the Fermat Point. Note that this point is a valid solution to the shortest total distance problem only for triangle with the greatest angle less then 120 degrees. N.B. all information are included in the metadata of this svg file.

 frame(-3.5, -6, 7.5, 7) B C A triangle(6, 75:, 35:) C B P equilateral A C Q equilateral B A R equilateral s = segment(A, P) t = segment(B, Q) u = segment(C, R) F = intersection(line(A, P), line(B, Q)) color(red) thickness(2) draw(s) draw(t) draw(u) draw(F) thickness(0.5) color(black) thickness(4) draw(B, C, A) thickness(0.25) draw(B, C, P, dashed) draw(A, C, Q, dashed) draw(B, A, R, dashed) mark(segment(A, B), simple) mark(segment(A, R), simple) mark(segment(B, R), simple) mark(segment(A, C), double) mark(segment(A, Q), double) mark(segment(C, Q), double) mark(segment(B, C), triple) mark(segment(B, P), triple) mark(segment(C, P), triple) 

# Run eukleides and compile it into en:PSTricks. # Paste the resulting code in the following en:TeX file and compile it into eps.

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