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Convex Hexagon

Source: 2008 MMO Problem #1

September 13, 2011
geometry unsolvedgeometry

Problem Statement

Let ABCDEFABCDEF be a convex hexagon such that all of its vertices are on a circle. Prove that ADAD, BEBE and CFCF are concurrent if and only if ABBC⋅CDDE⋅EFFA=1\frac {AB}{BC}\cdot\frac {CD}{DE}\cdot\frac {EF}{FA}= 1.
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