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Cono Sur Olympiad
Cono Sur Shortlist - geometry
1993.12
1993.12
Part of
Cono Sur Shortlist - geometry
Problems
(1)
lengths of 8 segments by 4 lines, diff. integers - 1993 Cono Sur Shortlist G12
Source:
10/24/2021
Given
4
4
4
lines in the plane such that there are not
2
2
2
parallel to each other or no
3
3
3
concurrent, we consider the following
8
8
8
segments: in each line we have
2
2
2
consecutive segments determined by the intersections with the other three lines. Prove that: a) The lengths of the
8
8
8
segments cannot be the numbers
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
1, 2, 3,4, 5, 6, 7, 8
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
in some order. b) The lengths of the
8
8
8
segments can be
8
8
8
different integers.
geometry
segments