KöMaL 2023 B5313

Triangle $ABC$ is acute angled, and $AC<AB<BC$. The centre of the circumscribed circle is $O$, the orthocentre is $M$. The perpendicular bisector of side $AB$ intersects line $AM$ at point $P$, and the circle $OMP$ intersects line $BM$ again at a point $Q$, different from $M$. Prove that line $BC$ is tangent to the circle $ABQ$.