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2022 Polish Junior Math Olympiad Finals P1

Source: 2022 Polish Junior Math Olympiad Finals P1

May 21, 2023
geometry

Problem Statement

Given is a square ABCDABCD with side length 11. Points KK, LL, MM, and NN, distinct from the vertices of the square, lie on segments ABAB, BCBC, CDCD, and DADA, respectively. Prove that the perimeter of at least one of the triangles ANKANK, BKLBKL, CLMCLM, DMNDMN is less than 22.