RMO 2015

Geometry Level 5

There are two circles with centres $X$ and $Y$.The circle with centre $X$ passes through $Y$. $A$ is any point on the circle with centre $Y$ and $M$ is the midpoint of $YA$. $B$ is another point on the circle with centre $Y$, such that $AB$ is parallel to $XM$. AB intersects the circle with centre $X$ at $L$. If $AL=\sqrt3 \text{ cm}$, then find the value of $AB$.