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    Point of Minimal Distance : Equilateral Triangle

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    Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.

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    https://brainmass.com/math/triangles/point-of-minimal-distance-equilateral-triangle-14416

    Solution Preview

    For any point in this equilateral triangular region, the sum of the distances to the sides of the triangle is the same.
    Suppose the triangle has 3 vertices ...

    Solution Summary

    It is proven concisely that the sum of distances from a point inside an equilateral triangle is constant.

    $2.49

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