Problem

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 11.2

Tags: combinatorial geometry, combinatorics



Points $A_1, A_2, \ldots, A_{2022}$ are chosen on a plane so that no three of them are collinear. Consider all angles $A_iA_jA_k$ for distinct points $A_i, A_j, A_k$. What largest possible number of these angles can be equal to $90^\circ$? Proposed by Anton Trygub