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geometry

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ABCD is a square of side length 1. E , F , G and H are the midpoints of AB , BC , CD and DA , respectively. The lines FA , AG , GB , BH , HC , CE , ED and DF determine a convex 8-gon. By symmetry, this octagon has equal sides. If s is the side length of the octagon, then s 2 can be expressed as a b , where a and b are coprime positive integers. What is the value of a+b ?

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