Geometry Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter
In the figure below, given a triangle
ABC and its orthic triangle DEF (AD, BE, and CF are the
altitudes of ABC). Let be H the orthocenter of ABC. (1) Prove that
angles A, BDF and EDC are equal, (2) Prove that AD is the angle bisector of
angle EDF, and (3) prove that H is the incenter of triangle DEF.
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