In a triangle $ABC$, the line symmetric to the median through $A$ with respect to the bisector of the angle at $A$ intersects $BC$ at $M$. Points $P$ on $AB$ and $Q$ on $AC$ are chosen such that $MP\parallel AC$ and $MQ\parallel AB$. Prove that the circumcircle of the triangle $MPQ$ is tangent to the line $BC$.