You may consider splitting your pipe into triangles and then finding triangle - circle intersection area. If they do intersect the intersection will always be a convex polygon (area is easy to calculate by splitting into triangles again) and a segment (area is easy to calculate too - http://en.wikipedia.org/wiki/Circular_segment ). The other case is the triangle itself, in case it lies inside the circle completely (a simple case again).
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.