In the figure below, given a triangle
ABC and its orthic triangle DEF (AD, BE, and CF are the
altitudes of ABC). L, M, N are the tangency points of the
incircle of triangle DEF and DG and DK
are perpendicular to BE and CF respectively. (1) Prove that GK is
parallel to EF and (2) prove that GK = DM = DN.
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