2016 UMO Problems/Problem 4

Problem

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 $\frac{AB}{FA}$ .

Solution

$\frac{3}{2}$

2016 UMO (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5 • 6
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2016 UMO Problems/Problem 4

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