NL-NWO 1993 Problem 2

In a triangle $ABC$ with $\angle A=90^{\circ}$ , $D$ is the midpoint of $BC$ , $F$ that of $AB$ , $E$ that of $AF$ and $G$ that of $FB$ . Segment $AD$ intersects $CE,CF$ and $CG$ in $P,Q$ and $R$ , respectively. Determine the ratio: $\frac{PQ}{QR}$ .