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An Inequality for Tripolar Coordinates Related to the Brocard Angle

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For a triangle and a point , let , and be the Brocard angle (Wolfram MathWorld) of .

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(The tripolar coordinates of with respect to are .)

Then ;

equality holds when is an acute triangle and is its Fermat point.

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Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

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