A trapezium ABCD, in which AB is parallel to CD, is inscribed in a circle with centre O. Suppose the diagonals AC and BD of the trapezium intersect at M, and OM \equal{} 2.
(a) If ∠AMB is 60∘, find, with proof, the difference between the lengths of the parallel sides.
(b) If ∠AMD is 60∘, find, with proof, the difference between the lengths of the parallel sides.
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