Geometry · Equiangular polygons · Centre of symmetry · Irrationality of root two · Parallelograms · Circumscribed rectangle · Convex polygons
An octagon has all of its interior angles equal, and the lengths of all of its sides are rational numbers. Prove that it has a centre of symmetry.
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Serbian Republic Competition (Republicko takmicenje) 1998, high school grade I, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source