A·
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.

A·
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).

A·
_____
_.--`"¯ ¯"`._
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