MathDB
Cyclic hexagon

Source:

July 19, 2006
geometry theoremsgeometry

Problem Statement

If ABCDEFABCDEF is a convex cyclic hexagon, then its diagonals ADAD, BEBE, CFCF are concurrent if and only if ABBC⋅CDDE⋅EFFA=1\frac{AB}{BC}\cdot \frac{CD}{DE}\cdot \frac{EF}{FA}=1. Alternative version. Let ABCDEFABCDEF be a hexagon inscribed in a circle. Then, the lines ADAD, BEBE, CFCF are concurrent if and only if AB⋅CD⋅EF=BC⋅DE⋅FAAB\cdot CD\cdot EF=BC\cdot DE\cdot FA.
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