Weighted sums of the squares of the distances of a point to the sidelines of a triangle
Ganchev, Georgi · Nikolov, Nikolai
Original · EN
We study a function, which is a weighted sum of the squares of the distances of an arbitrary point to the sidelines of a triangle. The given weights, considered as barycentric coordinates, determine a point M. We prove that the function reaches its minimum (maximum) at a point, which is isogonal conjugate to M.
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