In triangle $ABC$, points $P$ and $Q$ are projections of point $A$ onto the bisectors of angles $ABC$ and $ACB$, respectively. Prove that $PQ\parallel BC$.
Problem
Source: Indonesia INAMO Shortlist 2017 G3 https://artofproblemsolving.com/community/c1101409_indonesia_shortlist__geometry
Tags: geometry, parallel