Weighted sums of the squares of the distances of a point to the sidelines of a triangle

Georgi Ganchev; Nikolai Nikolov

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arXiv · 1604.05248

Weighted sums of the squares of the distances of a point to the sidelines of a triangle

Georgi Ganchev·Nikolai Nikolov

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Abstract

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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Georgi Ganchev, Nikolai Nikolov. 2016-04-15. Weighted sums of the squares of the distances of a point to the sidelines of a triangle. https://arxiv.org/abs/1604.05248

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