Difference between revisions of "2006 AMC 12A Problems/Problem 22"
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== Problem == | == Problem == | ||
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| + | 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>? | ||
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| + | <math> \mathrm{(A) \ } 2\sqrt{2}+2\sqrt{3}\qquad \mathrm{(B) \ } 3\sqrt{3}+\sqrt{2}</math><math>\mathrm{(C) \ } 2\sqrt{6}+\sqrt{3}\qquad \mathrm{(D) \ } 3\sqrt{2}+\sqrt{6}\qquad \mathrm{(E) \ } 6\sqrt{2}-\sqrt{3}</math> | ||
== Solution == | == Solution == | ||
Revision as of 23:08, 10 July 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 ?
