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 \(a+b.\)
by
Calvin Lin