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.
View or post a solution