MathDB
Many Right Angles

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

April 5, 2023
combinatorial geometrycombinatorics

Problem Statement

Points A1,A2,…,A2022A_1, A_2, \ldots, A_{2022} are chosen on a plane so that no three of them are collinear. Consider all angles AiAjAkA_iA_jA_k for distinct points Ai,Aj,AkA_i, A_j, A_k. What largest possible number of these angles can be equal to 90∘90^\circ?
Proposed by Anton Trygub
Back to ProblemsView on AoPS