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Problem A. 538. (May 2011)

A. 538. In the 3-dimensional hyperbolic space there are given a plane \mathcal{P} and four distinct lines a1, a2, r1, r2 in such positions that a1 and a2 are perpendicular to \mathcal{P}, r1 is coplanar with a1, r2 is coplanar with a2, finally r1 and r2 intersect \mathcal{P} at the same angle. Rotate r1 around a1 and rotate r2 around a2; denote by \mathcal{S}_1 and \mathcal{S}_2 the two surfaces of revolution they sweep out. Show that the common points of \mathcal{S}_1 and \mathcal{S}_2 lie in a plane.

(5 pont)

Deadline expired on 10 June 2011.


Statistics:

2 students sent a solution.
5 points:Backhausz Tibor.
4 points:Nagy 235 János.

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