IMO Shortlist 1995 problem G3

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The incircle of triangle \triangle ABC touches the sides BC, CA, AB at D, E, F respectively. X is a point inside triangle of \triangle ABC such that the incircle of triangle \triangle XBC touches BC at D, and touches CX and XB at Y and Z respectively.
Show that E, F, Z, Y are concyclic.
Izvor: Međunarodna matematička olimpijada, shortlist 1995