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2018 AMC 10B Problems/Problem 12

Revision as of 15:14, 16 February 2018 by Cardinals2014 (talk | contribs) (Created page with "Line segment <math>\overline{AB}</math> is a diameter of a circle with <math>AB=24</math>. Point <math>C</math>, not equal to <math>A</math> or <math>B</math>, lies on the cir...")
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Line segment $\overline{AB}$ is a diameter of a circle with $AB=24$. Point $C$, not equal to $A$ or $B$, lies on the circle. As point $C$ moves around the circle, the centroid (center of mass) of $\triangle{ABC}$ traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?

$\textbf{(A)} \text{ 25} \qquad \textbf{(B)} \text{ 38} \qquad \textbf{(C)} \text{ 50} \qquad \textbf{(D)} \text{ 63} \qquad \textbf{(E)} \text{ 75}$

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