Question 9
Point $M$ is the midpoint of side $AC$ of triangle $ABC$. Points $P$ and $Q$ are chosen on segments $AM$ and $CM$, respectively, so that $PQ=AC/2$. The circumcircle of triangle $ABQ$ meets side $BC$ at $X\ne B$, and the circumcircle of triangle $BCP$ meets side $AB$ at $Y\ne B$. Prove that quadrilateral $BYMX$ is cyclic. (F. Ivlev, F. Nilov)