IMO Shortlist 1998 problem G6
Dodao/la:
arhiva2. travnja 2012. Let
![ABCDEF](/media/m/9/f/e/9fe205b534135e3a700ffb54d8b96cb0.png)
be a convex hexagon such that
![\angle B+\angle D+\angle F=360^{\circ }](/media/m/3/c/5/3c50d6c9b683118227f6156c55431712.png)
and
![\frac{AB}{BC} \cdot \frac{CD}{DE} \cdot \frac{EF}{FA} = 1.](/media/m/8/4/3/8438134959fb6efaf32bfd6083fbc1b8.png)
Prove that
%V0
Let $ABCDEF$ be a convex hexagon such that $\angle B+\angle D+\angle F=360^{\circ }$ and $$\frac{AB}{BC} \cdot \frac{CD}{DE} \cdot \frac{EF}{FA} = 1.$$ Prove that $$\frac{BC}{CA} \cdot \frac{AE}{EF} \cdot \frac{FD}{DB} = 1.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1998