Difference between revisions of "2006 AMC 12A Problems/Problem 22"

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== See also ==
 
== See also ==
 
* [[2006 AMC 12A Problems]]
 
* [[2006 AMC 12A Problems]]
* [[2006 AMC 12A Problems/Problem 21 | Previous problem]]
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* [[2006 AMC 12A Problems/Problem 23 | Next problem]]
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{{AMC12 box|year=2006|ab=A|num-b=21|num-a=23}}
  
 
[[Category:Intermediate Geometry Problems]]
 
[[Category:Intermediate Geometry Problems]]

Revision as of 19:24, 2 February 2007

Problem

A circle of radius $r$ is concentric with and outside a regular hexagon of side length $2$. The probability that three entire sides of hexagon are visible from a randomly chosen point on the circle is $1/2$. What is $r$?

$\mathrm{(A) \ } 2\sqrt{2}+2\sqrt{3}\qquad \mathrm{(B) \ } 3\sqrt{3}+\sqrt{2}$$\rm{(C) \ } 2\sqrt{6}+\sqrt{3}\qquad \rm{(D) \ } 3\sqrt{2}+\sqrt{6}$

$\mathrm{(E) \ }  6\sqrt{2}-\sqrt{3}$

Solution

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See also

2006 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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All AMC 12 Problems and Solutions
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