Question 4
(GDR) In the interior of $\triangle P_1P_2P_3$ a point $P$ is given. Let $Q_1,Q_2$, and $Q_3$ respectively be the intersections of $PP_1,PP_2$, and $PP_3$ with the opposing edges of $\triangle P_1P_2P_3$. Prove that among the ratios $PP_1/PQ_1,PP_2/PQ_2$, and $PP_3/PQ_3$ there exists at least one not larger than $2$ and at least one not smaller than $2$.