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Splitting the Sides of a Triangle by Its Pedal Triangle

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

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Let , , be the exact trilinear coordinates (Wolfram MathWorld) of with respect to the sides , , ; let ; and let , , be Conway notation with respect to .

Then, as signed distances,

,

.

The formulas for the other two sides are analogous.

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

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