Question 97
Let $ABC$ be a right triangle with the right angle at $C$, such that $|BC| = a$ and $|AC| = b$. Let $D$ be a point on the opposite side of the line $AC$ from $B$, such that the triangle $ACD$ is similar to the triangle $ABC$. Let $E$ be a point on the line $CD$, such that $\angle EBC$ is a right angle. Find the area of the quadrilateral $ABED$ in terms of $a$ and $b$.