OME 2022 Problem 4

Let $P$ be a point in the plane. Prove that it is possible to draw three rays with origin in $P$ with the following property: for every circle with radius $r$ containing $P$ in its interior, if $P_1$ , $P_2$ and $P_3$ are the intersection points of the three rays with the circle, then $$|PP_1|+|PP_2|+|PP_3|\leq 3r.$$