Question 33
Let $P$ be a point in the plane. Prove that it is possible to draw three rays with origin $P$ with the following property: for every circle of radius $r$ that contains $P$ in its interior, if $P_1$, $P_2$ and $P_3$ are the intersection points of the rays with the circle, then
$$
|PP_1| + |PP_2| + |PP_3| \le 3r.
$$
$$
|PP_1| + |PP_2| + |PP_3| \le 3r.
$$