Question 14
The diagonals $AC$ and $BD$ of a convex quadrilateral $ABCD$ intersect at $E$ and $\frac{CE}{AC} = \frac{3}{7}$, $\frac{DE}{BD} = \frac{4}{9}$. Let $P$ and $Q$ be the points that divide the segment $BE$ into three equal parts, with $P$ between $B$ and $Q$, and let $R$ be the midpoint of the segment $AE$. Calculate $\frac{\text{area}(APQR)}{\text{area}(ABCD)}$.