MathNet 2017-part-07 — 172 problems (EN–VI) Question 83

Let $ABC$ be a triangle, $I$ the incenter, and $D$ the intersection of lines $AI$ and $BC$. The perpendicular bisector of $AD$ meets $BI$ and $CI$ at $P$ and $Q$. Show that $I$ is the orthocenter of triangle $PQD$.