Let $\vartriangle ABC$ be an equilateral triangle with side $1$. $1011$ points $P_1$, $P_2$, $P_3$, $...$, $P_{1011}$ on the side $AC$ and $1011$ points $Q_1$, $Q_2$, $Q_3$, $...$ ,$ Q_{1011}$ on side AB (see figure) in such a way as to generate $2023$ triangles of equal area. Find the length of the segment $AP_{1011}$. PS. Harder version of 2023 Chile NMO L1 P3
Problem
Source: 2023 Chile NMO L2 P3 - Senior version of 2023 Chile NMO L1 P3
Tags: geometry, Equilateral, areas
