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2017 CNMO Grade 11 P5

Source: 2017 China Northern MO, Grade 11, Problem 5

February 24, 2020
geometry

Problem Statement

Length of sides of regular hexagon ABCDEFABCDEF is aa. Two moving points M,NM,N moves on sides BC,DEBC,DE, satisfy that ∠MAN=π3\angle MAN=\frac{\pi}{3}. Prove that AM⋅AN−BM⋅DNAM\cdot AN-BM\cdot DN is a definite value.
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