Difference between revisions of "2006 AMC 12A Problems/Problem 22"
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== Problem == | == Problem == | ||
| − | A circle of radius <math>r</math> is concentric with and outside a regular hexagon of side length <math>2</math>. The probability that three entire sides of hexagon are visible from a randomly chosen point on the circle is <math>1/2</math>. What is <math>r</math>? | + | A [[circle]] of [[radius]] <math>r</math> is [[concentric]] with and outside a [[regular polygon | regular]] [[hexagon]] of side length <math>2</math>. The [[probability]] that three entire sides of hexagon are visible from a randomly chosen point on the circle is <math>1/2</math>. What is <math>r</math>? |
<math> \mathrm{(A) \ } 2\sqrt{2}+2\sqrt{3}\qquad \mathrm{(B) \ } 3\sqrt{3}+\sqrt{2}</math><math>\rm{(C) \ } 2\sqrt{6}+\sqrt{3}\qquad \rm{(D) \ } 3\sqrt{2}+\sqrt{6}</math> | <math> \mathrm{(A) \ } 2\sqrt{2}+2\sqrt{3}\qquad \mathrm{(B) \ } 3\sqrt{3}+\sqrt{2}</math><math>\rm{(C) \ } 2\sqrt{6}+\sqrt{3}\qquad \rm{(D) \ } 3\sqrt{2}+\sqrt{6}</math> | ||
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== Solution == | == Solution == | ||
| − | + | {{solution}} | |
== See also == | == See also == | ||
| + | * [[2006 AMC 12A Problems/Problem 21 | Previous problem]] | ||
| + | * [[2006 AMC 12A Problems/Problem 23 | Next problem]] | ||
* [[2006 AMC 12A Problems]] | * [[2006 AMC 12A Problems]] | ||
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| + | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 19:05, 3 November 2006
Problem
A circle of radius 
is concentric with and outside a regular hexagon of side length 
. The probability that three entire sides of hexagon are visible from a randomly chosen point on the circle is 
. What is ?
Solution
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