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Grand finale of 2021 Iberoamerican MO

Source: 2021 Iberoamerican Mathematical Olympiad, P6

October 20, 2021
geometrycongruent triangles

Problem Statement

Consider a nn-sided regular polygon, n≥4n \geq 4, and let VV be a subset of rr vertices of the polygon. Show that if r(r−3)≥nr(r-3) \geq n, then there exist at least two congruent triangles whose vertices belong to VV.
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