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2021 Iberoamerican
6
6
Part of
2021 Iberoamerican
Problems
(1)
Grand finale of 2021 Iberoamerican MO
Source: 2021 Iberoamerican Mathematical Olympiad, P6
10/20/2021
Consider a
n
n
n
-sided regular polygon,
n
≥
4
n \geq 4
n
≥
4
, and let
V
V
V
be a subset of
r
r
r
vertices of the polygon. Show that if
r
(
r
−
3
)
≥
n
r(r-3) \geq n
r
(
r
−
3
)
≥
n
, then there exist at least two congruent triangles whose vertices belong to
V
V
V
.
geometry
congruent triangles