A circle and a hexagon
Source: AMC 12 2006A, Problem 22
February 5, 2006
probabilitytrigonometryquadraticsgeometryrectanglesimilar trianglestrig identities
Problem Statement
A circle of radius 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 ?
(A) 2\sqrt {2} \plus{} 2\sqrt {3} \qquad (B) 3\sqrt {3} \plus{} \sqrt {2} \qquad (C) 2\sqrt {6} \plus{} \sqrt {3} \qquad (D) 3\sqrt {2} \plus{} \sqrt {6}\\
(E) 6\sqrt {2} \minus{} \sqrt {3}