AMC 10 2021-fall-b Problem 21

Regular polygons with $5,6,7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect? $(\textbf{A})\: 52 (\textbf{B}) \: 56 (\textbf{C}) \: 60 (\textbf{D}) \: 64 (\textbf{E}) \: 68$