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Prove that lines BD, FX and ME are concurrent?

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 & C. 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. Prove that lines BD, FX and ME are concurrent.

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 & C. 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. Prove that lines BD, FX and ME are concurrent.

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