Circles & Lines · Hard problem

Quadrilateral $ABCD$ has $A=(0,0)$, $B=(12,0)$, and $C=(12,9)$, and $D$ lies somewhere on the positive $y$-axis. The diagonals $\overline{AC}$ and $\overline{BD}$ are perpendicular. What is the area of quadrilateral $ABCD$?