Practice: Find The Distance Between The Skew Lines

Geometry Level 5

The base of a pyramid $$ABCS$$ is an equilateral triangle $$ABC$$ with a side length of $$4\sqrt{2}.$$ The edge $$SC$$ is perpendicular to the base and has length $$2.$$ Let $$D$$ and $$E$$ be the midpoints of $$AB$$ and $$BC$$ respectively. The (shortest) distance between the skew lines $$SE$$ and $$CD$$ can be written as $$\sqrt{\frac{a}{b}},$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a+b.$$

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