KöMaL 2021 B5155

The convex quadrilateral $ABCD$ has no parallel sides, and the intersection of lines $AB$ and $CD$ is $M$. Point $X$ is moving along the interior of side $AB$, and point $Y$ is moving along the interior of side $CD$ so that the equality $AX:XB=DY:YC$ remains true. Show that the circles $MXY$ all have another common point, different from $M$.