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BWM 2013 P7: Hexagon whose vertices lie on a circle

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June 6, 2014

Problem Statement

Let ABCDEFABCDEF be a convex hexagon whose vertices lie on a circle. Suppose that AB⋅CD⋅EF=BC⋅DE⋅FAAB\cdot CD\cdot EF = BC\cdot DE\cdot FA. Show that the diagonals AD,BEAD, BE and CFCF are concurrent.
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