KöMaL 2019 C1568

Let $D$ be the midpoint of side $AB$ of a triangle $ABC$, $E$ the midpoint of side $AC$, and $P$, $Q$ the centres of the circumscribed circles of triangles $DEB$ and $DEC$, respectively (assume that $P\ne Q$). Prove that line $PQ$ is perpendicular to line $BC$.