Question 46
Let $M$ be the midpoint of the side $AC$ of a triangle $ABC$. The points $P$ and $Q$ are chosen on the segments $AM$ and $MC$, respectively, so that $PQ = AC/2$. The circumcircle of the triangle $ABQ$ meets the side $BC$ at $X \neq B$, while the circumcircle of the triangle $BCP$ meets the side $AB$ at $Y \neq B$. Prove that the quadrilateral $BXMY$ is cyclic. (F. Ivlev, F. Nilov)