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2001 Spain Mathematical Olympiad
Problem 3
Problem 3
Part of
2001 Spain Mathematical Olympiad
Problems
(1)
2001 Spanish Mathematical Olympiad, Problem 3
Source: Spanish Mathematical Olympiad 2001
6/6/2017
You have five segments of lengths
a
1
,
a
2
,
a
3
,
a
4
,
a_1, a_2, a_3, a_4,
a
1
,
a
2
,
a
3
,
a
4
,
and
a
5
a_5
a
5
such that it is possible to form a triangle with any three of them. Demonstrate that at least one of those triangles has angles that are all acute.
triangle inequality
geometry