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Centroid locus on circle diameter

1425ApprenticeCoordinate GeometryGeometry

AMC 12B · 2018 · Problem 8

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?

Answer choices

A
25
B
38
C
50
D
63
E
75
0 students attempted0% solvedRating 1425

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