Question 143
Let $ABCD$ be a convex quadrangle and $K$ be the point of intersection of its diagonals. If the points $L \in [AD]$, $M \in [AC]$, $N \in [BC]$ satisfy the conditions $KL \parallel AB$, $LM \parallel DC$, $MN \parallel AB$, show that
$$
\frac{\text{Area}(KLMN)}{\text{Area}(ABCD)} \lt \frac{8}{27}.
$$
$$
\frac{\text{Area}(KLMN)}{\text{Area}(ABCD)} \lt \frac{8}{27}.
$$