Question 99
In a circle, two non-intersecting chords $AB$ and $CD$ are drawn. On the chord $AB$, a point $E$ (different from $A$ and $B$) is taken. Consider the arc $AB$ that does not contain the points $C$ and $D$. With a compasses and a straightedge, find a point $F$ on that arc such that $\frac{PE}{EQ} = \frac{1}{2}$, where $P$ and $Q$ are the points in which the chord $AB$ meets the segments $FC$ and $FD$ respectively.