MathDB
AMC 10B #11

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November 17, 2021
AMCAMC 10AMC 10 B

Problem Statement

A regular hexagon of side length 11{ } is inscribed in a circle. Each minor arc of the circle determined by a side of the hexagon is reflected over that side. What is the area of the region bounded by these 66 reflected arcs?
(<spanclass=latexbold>A</span>)532π(<spanclass=latexbold>B</span>)33π(<spanclass=latexbold>C</span>)433π2(<spanclass=latexbold>D</span>)π32(<spanclass=latexbold>E</span>)π+32(<span class='latex-bold'>A</span>)\: \frac{5\sqrt{3}}{2} - \pi\qquad(<span class='latex-bold'>B</span>) \: 3\sqrt{3}-\pi\qquad(<span class='latex-bold'>C</span>) \: 4\sqrt{3}-\frac{3\pi}{2}\qquad(<span class='latex-bold'>D</span>) \: \pi - \frac{\sqrt{3}}{2}\qquad(<span class='latex-bold'>E</span>) \: \frac{\pi + \sqrt{3}}{2}