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Convex hexagon with all sides of length 1

Source: Romanian TST 1 2008, Problem 3

May 1, 2008
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCDEF ABCDEF be a convex hexagon with all the sides of length 1. Prove that one of the radii of the circumcircles of triangles ACE ACE or BDF BDF is at least 1.
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