MathNet 2019-part-07 — 184 problems (EN–VI) Question 47

In an acute triangle $ABC$, let $D$ be the midpoint of $[BC]$ and $P$ be a point on $[AD]$. The interior angle bisectors of $ABP$ and $ACP$ intersect at $Q$. Let $BQ \perp QC$. Prove that $Q \in [AP]$.