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AP + BM+CN= fixed, equilateral related

Source: Polish MO Finals 1959 p2

August 29, 2024
geometryfixedEquilateral

Problem Statement

In an equilateral triangle ABC ABC , point O O is chosen and perpendiculars OM OM , ON ON , OP OP are dropped to the sides BC BC , CA CA , AB AB , respectively. Prove that the sum of the segments AP AP , BM BM , CN CN does not depend on the position of point O O .
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