Go Geometry Problem Problem 324: Quadrilateral with perpendicular diagonals, Concurrence

The figure shows a quadrilateral ABCD with perpendicular diagonals intersecting at E. EF, EG, EH and EM are perpendicular to AB, BC, CD, and AD, respectively. Prove that lines FG, AC, and MH are concurrent.
 

  Quadrilateral, perpendicular diagonals

 

 

 

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