Splitting the Sides of a Triangle by Its Pedal Triangle

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 .
Let , , be the exact trilinear coordinates 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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