KöMaL 2023 C1774

$AB\parallel{CD}$ in a trapezium $ABCD$. The midpoints of sides $AB$ and $CD$ are $E$ and $F$, and line segments $DE$, $DB$, $FB$ intersect diagonal $AC$ at points $P$, $Q$, $R$, respectively. Prove that $\frac{CP}{PA}\cdot \frac{CQ}{QA} \cdot \frac{CR}{RA}= \left(\frac{CD}{AB}\right)^{ 3}$.