Question 33
$ABCD$ is a convex quadrilateral. $X$ lies on the segment $AB$ with $AX/XB = m/n$. $Y$ lies on the segment $CD$ with $CY/YD = m/n$. $AY$ and $DX$ intersect at $P$, and $BY$ and $CX$ intersect at $Q$. Show that $$\frac{\text{area } XQYP}{\text{area } ABCD} \lt \frac{mn}{m^2 + mn + n^2}.$$