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Inequality for a Cevian Involving the Circumradius

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Let be a triangle; define , , and let be the circumcircle of .

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For a point , let , , be signed areas and set , the barycentric coordinates of , so that .

Let .

Then , with equality if and only if is on .

You can drag the vertices , , .

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

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