ISL 1995 A4

Find all of the positive real numbers like $x,y,z,$ such that :

1.) $x + y + z = a + b + c$

2.) $4xyz = a^2x + b^2y + c^2z + abc$

Proposed to Gazeta Matematica in the 80s by VASILE CÎRTOAJE and then by Titu Andreescu to IMO 1995.