2006 AMC 12A Problems/Problem 22

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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2006 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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2006 AMC 12A Problems/Problem 22

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