A pentagonal pyramid has a "regular" base whose edges measure 100 metres each. The sloping edges are all different. They are known and they are (in order) 130,120 and 110 metres. What are the lengths of edges 4 and 5, and if the pyramid could be rotated on a vertical axis (which is perpendicular to the base and at its centre) what would be the diameter of the circle described by the apex of the pyramid.?