Steiner Point

When given 3 points A B C in a Triangle

 A·----110m---·B
   \         /
    \  s·   /
     \   190m
     200m /
       \ /
        V
        ·
         C

The Steiner Point is the point within the triangle that connects the 3 corner nodes of the triangle into a Steiner Tree, and does so with the minimum overhead (in this case, distance).
This point is NOT equidistant from A, B, and C. Instead, angles ASB, BSC, and CSA are all 120 degrees. To easilly find this point, use Torricelli's Method of finding a Steiner Point.

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10998521 is entirely correct in calling it the Fermat point. The Steiner Point is another alias, popularized by Courant and Robbins in What is Mathematics (1941), calling it the Steiner Minimal Tree problem.

The identification of this point was posed as a challenge by Pierre de Fermat to Evangelista Torricelli. For this reason, the point is usually known as the Fermat point or the Fermat-Torricelli point.

The usual construction of this point is, given the triangle ABC, to construct a point D, on the opposite side of BC to A, such that BCD is equilateral. The Fermat/Fermat-Torricelli/Steiner point is the intersection of AD with the circumcircle of BCD.