RMO 2015

Geometry Level 5

There are two circles with centres XX and YY.The circle with centre XX passes through YY. AA is any point on the circle with centre YY and MM is the midpoint of YAYA. BB is another point on the circle with centre YY, such that ABAB is parallel to XMXM. AB intersects the circle with centre XX at LL. If AL=3 cmAL=\sqrt3 \text{ cm} , then find the value of ABAB.

Give your answer to 2 decimal places.

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