Školjka

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 $ADB$ and $ADC$ respectively. Let $P$ be a point on the line segment $\overline{BC}$ such that the points $P, Q, R, D$ are concyclic. Prove that the line $AP, BQ, CR$ are concurrent.