2016 IMO Problems/Problem 1

Triangle BCF has a right angle at B.Let A be the point on line CF such that FA=FB and F lies between C and A. Point D is chosen such that DA=DC and AC is the bisector of ∠DAB. Point E is chosen such that EA=ED and AD is the bisector of ∠EAC. Let M be the midpoint of CF . Let X be the point such that AMXE is a parallelogram (where AM||EX and AE||MX). Prove that the lines BD,FX and ME are concurrent.

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