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proof in a square, arbitrary line (2001 Moldova MO Grade 7 P3)

Source:

April 12, 2021
geometry

Problem Statement

A line di (i=1,2,3)d_i~(i=1,2,3) intersects two opposite sides of a square ABCDABCD at points MiM_i and NiN_i. Prove that if M1N1=M2N2=M3N3M_1N_1=M_2N_2=M_3N_3, then two of the lines did_i are either parallel or perpendicular.
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