Mathematical and Physical Journal
for High Schools
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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 June 10, 2011.

Statistics:

2 students sent a solution.

5 points: Backhausz Tibor.

4 points: Nagy 235 János.

Problems in Mathematics of KöMaL, May 2011

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