2016 UMO Problems/Problem 4


Equiangular hexagon $ABCDEF$ has $AB = CD = EF$ and $AB > BC$. Segments $AD$ and $CF$ intersect at point $X$ and segments $BE$ and $CF$ intersect at point $Y$ . If quadrilateral $ABYX$ can have a circle inscribed inside of it (meaning there exists a circle that is tangent to all four sides of the quadrilateral), then find $\frac{AB}{FA}$.



See Also

2016 UMO (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6
All UMO Problems and Solutions