IMO Shortlist 2016 problem G1

  Avg: 0,0
  Avg: 6,0

Triangle BCF has a right angle at B. Let A be the point on line CF such that FA=FB and F lies between A and C. Point D is chosen so that DA=DC and AC is the bisector of \angle{DAB}. Point E is chosen so that EA=ED and AD is the bisector of \angle{EAC}. Let M be the midpoint of CF. Let X be the point such that AMXE is a parallelogram. Prove that BD,FX and ME are concurrent.