MEMO 2018 I3

Let $ABC$ be an acute-angled triangle with $AB<AC,$ and let $D$ be the foot of its altitude from $A.$ Let $R$ and $Q$ be the centroids of triangles $ABD$ and $ACD$ , respectively. Let $P$ be a point on the line segment $BC$ such that $P \neq D$ and points $P$ $Q$ $R$ and $D$ are concyclic .Prove that the lines $AP$ $BQ$ and $CR$ are concurrent.