IMO 1968 — Shortlist problems Question 17

(GBR 4) Given a point $O$ and lengths $x,y,z$, prove that there exists an equilateral triangle $ABC$ for which $OA=x,OB=y,OC=z$, if and only if $x+y\ge z,y+z\ge x,z+x\ge y$ (the points $O,A,B,C$ are coplanar).