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startng with trisectors of angles <A, <B in a parallelogram ABCD

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P4

August 2, 2018
parallelogramgeometryanglesEquilateral Triangle

Problem Statement

In a parallelogram ABCDABCD the trisectors of angles AA and BB are drawn. Let OO be the common points of the trisectors nearest to ABAB. Let AOAO meet the second trisector of angle BB at point A1A_1, and let BOBO meet the second trisector of angle AA at point B1B_1. Let MM be the midpoint of A1B1A_1B_1. Line MOMO meets ABAB at point NN Prove that triangle A1B1NA_1B_1N is equilateral.
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