Difference between revisions of "2016 UMO Problems/Problem 4"
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==Problem == | ==Problem == | ||
| + | Equiangular hexagon <math>ABCDEF</math> has <math>AB = CD = EF</math> and <math>AB > BC</math>. Segments <math>AD</math> and <math>CF</math> intersect at point <math>X</math> and segments <math>BE</math> and <math>CF</math> intersect at point <math>Y</math> . If quadrilateral <math>ABYX</math> 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 <math>\frac{AB}{FA}</math>. | ||
== Solution == | == Solution == | ||
| + | |||
| + | <math>\frac{3}{2}</math> | ||
== See Also == | == See Also == | ||
{{UMO box|year=2016|num-b=3|num-a=5}} | {{UMO box|year=2016|num-b=3|num-a=5}} | ||
| − | [[Category:]] | + | [[Category: Intermediate Geometry Problems]] |
Latest revision as of 04:11, 22 January 2019
Problem
Equiangular hexagon 
has 
and 
. Segments 
and 
intersect at point 
and segments 
and intersect at point 
. If quadrilateral 
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 
.
Solution
See Also
| 2016 UMO (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All UMO Problems and Solutions | ||
