Max area quadrilateral equilateral centroid triangle

1675AdeptCoordinate GeometryGeometryOptimization

AMC 12B · 2019 · Problem 25

Let $ABCD$ be a convex quadrilateral with $BC=2$ and $CD=6.$ Suppose that the centroids of $\triangle ABC,\triangle BCD,$ and $\triangle ACD$ form the vertices of an equilateral triangle. What is the maximum possible value of the area of $ABCD$?

Answer choices

16\sqrt3

12+10\sqrt3

9+12\sqrt3

0 students attempted0% solvedRating 1675

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