2021 OIM Problems/Problem 6

Problem

Consider a regular polygon with $n$ sides, $n \ge 4$, and let $V$ be a subset of $r$ vertices of the polygon. Show that if $r(r - 3) \ge n$, then there exist at least two congruent triangles whose vertices are in $V$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://olcoma.ac.cr/internacional/oim-2021/examenes