Let M be the circumcenter of ΔABC ( ∠B = 90° ),
    E the point on altitude BD of ΔABC such that 
      ∠AEC = 135°,
    F the point such that BDCF is a rectangle. and
    G the intersection of line segment MF and the
      circumcircle of ΔABC.

Prove that |DE| = |FG|.