Question

why is it possible to draw a circle which passes through all vertices of a rectangle

Answer 1

Any point on the perpendicular bisector of each side is equidistant from the two vertices involved. Therefore the intersection of these is equidistant from all. Thus the center of the "circumcenter" is at the intersection of perpendicular bisectors. See:
http://en.wikipedia.org/wiki/Circumscribed_circle