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| − | ==Problem ==
| + | #REDIRECT [[2018_AMC_10B_Problems/Problem_12]] |
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| − | 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 circle. As point <math>C</math> moves around the circle, the centroid (center of mass) of (insert triangle symbol)<math>ABC</math> traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?
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| − | <math>\textbf{(A)} \indent 25 \qquad \textbf{(B)} \indent 32 \qquad \textbf{(C)} \indent 50 \qquad \textbf{(D)} \indent 63 \qquad \textbf{(E)} \indent 75 </math>
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| − | ==Solution==
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| − | Draw the Median connecting C to the center O of the circle. Note that the centroid is <math>\frac{1}{3}</math> of the distance from O to C.
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| − | Thus, as C traces a circle of radius 12, the Centroid will trace a circle of radius <math>\frac{12}{3}=4</math>.
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| − | The area of this circle is <math>\pi\cdot4^2=16\pi \approx \boxed{50}</math>.
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| − | ==See Also==
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| − | {{AMC12 box|year=2018|ab=B|num-a=9|num-b=7}}
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| − | {{MAA Notice}}
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