The Product of the Perpendiculars to the Sides of a Triangle

The tangential triangle of a triangle ABC is the triangle (A'B'C' in the figure) formed by the tangents to the circumcircle of ABC at A, B, and C.
The product of the distances from a point P on the circumcircle of a triangle ABC to its sides equals the product of the distances of P to the sides of the tangential triangle A'B'C': .

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See Problem 4 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 65.
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