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 \(AB\).

Give your answer to 2 decimal places.

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