Difference between revisions of "2006 AMC 12A Problems/Problem 22"
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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>? | 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>? | ||
| − | <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} | + | <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}</math><math>\mathrm{(E) \ } 6\sqrt{2}-\sqrt{3}</math> |
== Solution == | == Solution == | ||
Revision as of 23:09, 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 ?
