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France Contests
French Mathematical Olympiad
1998 French Mathematical Olympiad
Problem 5
Problem 5
Part of
1998 French Mathematical Olympiad
Problems
(1)
existence of subset of points inside triangle
Source: 1998 France MO P5
4/10/2021
Let
A
A
A
be a set of
n
≥
3
n\ge3
n
≥
3
points in the plane, no three of which are collinear. Show that there is a set
S
S
S
of
2
n
−
5
2n-5
2
n
−
5
points in the plane such that, for each triangle with vertices in
A
A
A
, there exists a point in
S
S
S
which is strictly inside that triangle.
geometry
combinatorics