DE-BUNDESWETTBEWERB 2010 Problem 7

Given an acute-angled triangle $ABC$ . Let $CB$ be the altitude and $E$ a random point on the line $CD$ . Finally, let $P, Q, R$ and $S$ are the projections of $D$ on the straight lines $AC, AE, BE$ and $BC$ . Prove that the points $P, Q, R$ and $S$ lie either on a circle or on one straight line.