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Exact Trilinear Coordinates and the Pedal Triangle

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Given a triangle and a point , let be the feet of the perpendiculars from to the sides of . is called the pedal triangle of for .

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Let , , be the exact trilinear coordinates of with respect to the sides , , , which have side lengths , , . Let be the inradius and be the semiperimeter of .

Then

,

with equality if and only if is the circumcenter of .

You can drag the points , , and .

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

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