Question 49
Let $ABCD$ be a cyclic quadrilateral with $AB=3$, $BC=2$, $CD=2$, $DA=4$. Let lines perpendicular to $\overline{BC}$ from $B$ and $C$ meet $\overline{AD}$ at $B'$ and $C'$, respectively. Let lines perpendicular to $\overline{AD}$ from $A$ and $D$ meet $\overline{BC}$ at $A'$ and $D'$, respectively. Compute the ratio $\frac{[BCC'B']}{[DAA'D']}$, where $[\varpi]$ denotes the area of figure $\varpi$.