11.2

Part of 2023 Ukraine National Mathematical Olympiad

Problems(1)

Many Right Angles

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

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

combinatorial geometrycombinatorics