Question 105
Let $ABCD$ be a square (vertices labelled in clockwise order). Let $Z$ be any point on diagonal $AC$ between $A$ and $C$ such that $AZ \gt ZC$. Points $X$ and $Y$ exist such that $AXYZ$ is a square (vertices labelled in clockwise order) and point $B$ lies inside $AXYZ$. Let $M$ be the point of intersection of lines $BX$ and $DZ$ (extended if necessary). Prove that $C$, $M$ and $Y$ are collinear.