Problem 1401

Let $ABC$ be a triangle, with an obtuse angle at $A$. Let $Q$ be a point (other than $A$, $B$ or $C$) on the circumcircle of the triangle, on the same side of chord $BC$ as $A$, and let $P$ be the other end of the diameter through $Q$. Let $V$ and $W$ be the feet of the perpendiculars from $Q$ onto $CA$ and $AB$ respectively. Prove that the triangles $PBC$ and $AWV$ are similar. [Note: the circumcircle of the triangle $ABC$ is the circle which passes through the vertices $A$, $B$ and $C$.]