Question 77
Let $ABCD$ be a convex quadrilateral. Let $E$ and $F$ be points on the sides $AB$ and $CD$, respectively, such that $AB : AE = CD : DF = n$. If $S$ is the area of the quadrilateral $AEFD$, show that
$$
S \le \frac{AB \cdot CD + n(n-1)DA^2 + nDA \cdot BC}{2n^2}.
$$
$$
S \le \frac{AB \cdot CD + n(n-1)DA^2 + nDA \cdot BC}{2n^2}.
$$