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Miklós Schweitzer
2018 Miklós Schweitzer
10
10
Part of
2018 Miklós Schweitzer
Problems
(1)
Covering common points
Source: Miklós Schweitzer 2018 P10
11/18/2018
In 3-dimensional hyperbolic space, we are given a plane
P
P
P
and four distinct straight lines: the lines
a
1
a_1
a
1
and
a
2
a_2
a
2
are perpendicular to
P
P
P
; while the lines
r
1
r_1
r
1
and
r
2
r_2
r
2
do not intersect
P
P
P
, and their distances from
P
P
P
are equal. Denote by
S
i
S_i
S
i
the surface of revolution obtained by rotating
r
i
r_i
r
i
around
a
i
a_i
a
i
. Show that the common points of
S
1
S_1
S
1
and
S
2
S_2
S
2
can be covered by two planes.
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