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midpoint of orthocenters, trapezoid- Austrian-Polish 1997, 2003 Rioplatense L1p2

Source:

May 19, 2019
geometrytrapezoidorthocentermidpoint

Problem Statement

In a trapezoid ABCDABCD with AB//CDAB // CD, the diagonals ACAC and BDBD intersect at point EE. Let FF and GG be the orthocenters of the triangles EBCEBC and EADEAD. Prove that the midpoint of GFGF lies on the perpendicular from EE to ABAB.
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