A castle is at the center of the several flat paths which surround it: 4 straight paths that travel from the castle to its circular moat, where they meet up with a perfectly circular path which borders the moat; that circular path circumscribes a square path which has its corners at the ends of the 4 straight paths-see the diagram above. If the total length of all of the pathways is "q" kilometers, then which expression represents the distance from the castle to the circular moat?

A) q / 4(2+2*sqrt(2)+pi) km
B) q / 2(2+2*sqrt(2)+pi) km
C) q / (2+2*sqrt(2)+pi) km
D) 2q / (2+2*sqrt(2)+pi) km
E) 4q / (2+2*sqrt(2)+pi) km

[spoiler]OA=B[/spoiler]

Source: Manhattan Prep