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C·                   ·B
Pierre de Fermat first gave the problem, "Find the point in a triangle where the sum of its distances to the three vertices is minimal". Torricelli is credited with being the first to find a solution to this problem.

Torricelli's Method Begins by making the equilateral triangle of 2 of the 3 points and X, where angle AC intersects XC at C, and AB intersects XB at B.
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C·                   ·B








          ·X
Circumscribe a circle containing points C, B, and X (no, i'm not about to try and draw all of this in ascii).
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   _.--`"¯     ¯"`._ 
C·`                 `·B 
                     






          ·X
Point S exists where line AX intersects the circle containing points CBX.
    A·
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      \ 
       \  _____              
   _.--·"¯     ¯"`._ 
C·`    \S           `·B 
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          ·X

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