Geometry Problem 138. Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.
In the figure below, given a triangle
ABC of circumcenter O and its orthic triangle DEF (AD, BE, and CF are the
altitudes of ABC). Prove that OA, OB, and OC are perpendicular
to EF, DF, and DE respectively.
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