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Point of Minimal Distance : Equilateral Triangle

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.

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.

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