Let $ AB$ and $ CD$ be two disjoint chords of a circle. A point $ E$, distinct from $ A$ and $ B$, is taken on the chord $ AB$. Consider the arc $ AB$ not containing $ C$ and $ D$. Using a ruler and a compass, construct a point $ F$ on this arc such that $ \frac{PE}{EQ}=\frac{1}{2}$, where $ P$ and $ Q$ are the intersection points of $ AB$ with the segments $ FC$ and $ FD$, respectively.