MathDB

2008.8

Part of Swiss NMO - geometry

Problems(1)

diagonals' concurrency criterion in a cyclic hexagon

Source: Switzerland - Swiss MO 2008 p8

7/17/2020
Let ABCDEFABCDEF be a convex hexagon inscribed in a circle . Prove that the diagonals AD,BEAD, BE and CFCF intersect at one point if and only if ABBC⋅CDDE⋅EFFA=1\frac{AB}{BC} \cdot \frac{CD}{DE}\cdot \frac{EF}{FA}=1
geometryhexagonCyclicconcurrencyconcurrentdiagonals