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An Excircle Inequality

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For a triangle , let , , be the side lengths; be the incircle; be the circumcircle; and be the excircle opposite .

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Then ,

with equality if and only if is an isosceles triangle to vertex A.

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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