Problem 5, 2014

Let \(ABC\) be a right triangle with its right angle at \(C\), and write \(|BC| = a\), \(|AC| = b\). Let \(D\) be a point on the opposite side of the line \(AC\) from \(B\) for which the triangle \(ACD\) is similar to the triangle \(ABC\), the vertices corresponding in the order written. Let \(E\) be the point of the line \(CD\) for which the angle \(\angle EBC\) is right. Express the area of the quadrilateral \(ABED\) in terms of \(a\) and \(b\).