MathNet 2009-part-02 — 175 problems (EN–VI) Question 152

Let $ABC$ be a triangle, let $P$ be the midpoint of $BC$ and let $Q$ be a point on segment $CA$ such that $|CQ|=2|QA|$. Let $S$ be the intersection of $BQ$ and $AP$. Prove that $|AS|=|SP|$.