MEDAL!!!! In the figure about, point A is the center of the circle and a vertex of the right triangle, which has an area of 12 square units and where angle BAC is the right. Point D (not shown) is the point of intersection of the perimeter of circle A and segment An. The ratio of Ab to AC is 2 to 3 and the ratio of AD and AB is 1 to 2. What is the area of the shaded region, in square units?

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MEDAL!!!! In the figure about, point A is the center of the circle and a vertex of the right triangle, which has an area of 12 square units and where angle BAC is the right. Point D (not shown) is the point of intersection of the perimeter of circle A and segment An. The ratio of Ab to AC is 2 to 3 and the ratio of AD and AB is 1 to 2. What is the area of the shaded region, in square units?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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