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α/β is a rational number in regular 1996-gon

Source: Baltic Way 1996 Q1

March 19, 2011
geometry proposedgeometry

Problem Statement

Let α\alpha be the angle between two lines containing the diagonals of a regular 19961996-gon, and let β≠0\beta\not= 0 be another such angle. Prove that αβ\frac{\alpha}{\beta} is a rational number.
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