Points Symmetric to the Orthocenter with Respect to the Sides of a Triangle

Let ABC be a triangle. The points A', B', and C' symmetric to the orthocenter H with respect to the sides of ABC lie on the circumcircle. (A'', B'', and C'' are the feet of the perpendiculars from H to BC, CA, and AB, respectively.)



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See problem 5.9 in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).
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