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Exact Trilinear Coordinates and the Brocard Axis

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Given a triangle , let be the circumcenter and be the symmedian point. These points determine the Brocard axis (shown in orange).

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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 , , of length , , , respectively.

Let , let be the circumradius and let . When is the Brocard angle, .

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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