Practice: Find The Distance Between The Skew Lines

Geometry Level 4

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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