DK-GEORGMOHR 1996 Problem 1

In triangle $ABC$ , angle $C$ is right and the two catheti are both length $1$ . For one given the choice of the point $P$ on the cathetus $BC$ , the point $Q$ on the hypotenuse and the point $R$ are plotted on the second cathetus so that $PQ$ is parallel to $AC$ and $QR$ is parallel to $BC$ . Thereby the triangle is divided into three parts. Determine the locations of point $P$ for which the rectangular part has a larger area than each of the other two parts.