IMO Shortlist 1995 problem G3


Kvaliteta:
  Avg: 3,5
Težina:
  Avg: 7,0
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