OMM 1993 Problem 1

$ABC$ is a triangle with $\angle A = 90^o$ . Take $E$ such that the triangle $AEC$ is outside $ABC$ and $AE = CE$ and $\angle AEC = 90^o$ . Similarly, take $D$ so that $ADB$ is outside $ABC$ and similar to $AEC$ . $O$ is the midpoint of $BC$ . Let the lines $OD$ and $EC$ meet at $D'$ , and the lines $OE$ and $BD$ meet at $E'$ . Find area $DED'E'$ in terms of the sides of $ABC$ .