A. 538. In the 3-dimensional hyperbolic space there are given a plane and four distinct lines a1, a2, r1, r2 in such positions that a1 and a2 are perpendicular to , r1 is coplanar with a1, r2 is coplanar with a2, finally r1 and r2 intersect at the same angle. Rotate r1 around a1 and rotate r2 around a2; denote by and the two surfaces of revolution they sweep out. Show that the common points of and lie in a plane.
Deadline expired on 10 June 2011.