Problem

Source: Kvant Magazine No. 1 2023 M2733

Tags: Kvant, geometry



A convex 51-gon is given. For each of its vertices and each diagonal that does not contain this vertex, we mark in red a point symmetrical to the vertex relative to the middle of the diagonal. Prove that strictly inside the polygon there are no more than 20400 red dots. Proposed by P. Kozhevnikov