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An Inequality Relating the Nagel Point and Exact Trilinear Coordinates

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Given a triangle , let be the circumcenter and be the Nagel point. (See the MathWorld related link for the definition of the Nagel point.)

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For a point , the vertices of the pedal triangle of with respect to are the feet of the perpendiculars from to the sides of .

Let , , be the exact trilinear coordinates of with respect to the sides , , and let .

Let , be the circumradius and inradius of and let .

Then

.

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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