Question 16
(BLR) In an acute-angled triangle $ABC$, let $AD,BE$ be altitudes and $AP,BQ$ internal bisectors. Denote by $I$ and $O$ the incenter and the circumcenter of the triangle, respectively. Prove that the points $D,E,I$ are collinear if and only if the points $P,Q,O$ are collinear.