IR-MO 1997 Problem 5

In an acute triangle $ABC$ let $AD$ and $BE$ be altitudes, and $AP$ and $BQ$ be bisectors. Let $I$ and $O$ be centers of incircle and circumcircle, respectively. Prove that the points $D, E$ , and $I$ are collinear if and only if the points $P, Q$ , and $O$ are collinear.