HMMT 2021 G5

Let $A E F$ be a triangle with $E F=20$ and $A E=A F=21$. Let $B$ and $D$ be points chosen on segments $A E$ and $A F$, respectively, such that $B D$ is parallel to $E F$. Point $C$ is chosen in the interior of triangle $A E F$ such that $A B C D$ is cyclic. If $B C=3$ and $C D=4$, then the ratio of areas $\frac{[A B C D]}{[A E F]}$ can be written as $\frac{a}{b}$ for relatively prime positive integers $a, b$. Compute $100 a+b$.