Problem A. 538. (May 2011)
A. 538. In the 3dimensional hyperbolic space there are given a plane and four distinct lines a_{1}, a_{2}, r_{1}, r_{2} in such positions that a_{1} and a_{2} are perpendicular to , r_{1} is coplanar with a_{1}, r_{2} is coplanar with a_{2}, finally r_{1} and r_{2} intersect at the same angle. Rotate r_{1} around a_{1} and rotate r_{2} around a_{2}; denote by and the two surfaces of revolution they sweep out. Show that the common points of and lie in a plane.
(5 pont)
Deadline expired on 10 June 2011.
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