# Trapped inside a trapezium

Geometry Level 3

A trapezium $$ABCD$$ ( with $$AB || CD$$ ) is inscribed inside a circle of centre $$O$$ and its diagonals $$AC$$ and $$BD$$ intersect each other at $$M$$. If $$OM = 2$$ and $$\angle AMB = 60 ^\circ$$, then find the difference between the parallel sides.

If your answer is $$p\sqrt q$$, where $$p$$ and $$q$$ are positive integers with $$q$$ square-free, submit $$p+q$$.

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