Fermat point

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The point with the minimum total distance to the three vertices of a triangle. If the angle at any of the vertices is more than 120° then that vertex is the Fermat point, otherwise it is found by constructing an equilateral triangle on each of the three sides of the triangle. For each side of the triangle, join the new vertex of the equilateral triangle to the vertex in the original triangle which is not used in the side. These three lines intersect at the Fermat point. In the diagram X is the Fermat point.

Fermat point

Subjects: Mathematics.

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