Fermat point
From AoPSWiki
The Fermat point (also called the Torricelli point) of a triangle 
is a point 
which has the minimum total distance to three vertices (i.e., 
).
Construction
A method to find the point is to construct three equilateral triangles out of the three sides from , then connect each new vertex to each opposite vertex, as these three lines will concur at first Fermat point.
See Also
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