{"status": "success", "data": {"description_md": "Let $AB$ be a diameter of a circle and let $C$ be a point on $AB$ with $2\\cdot AC=BC$. Let $D$ and $E$ be points on the circle such that $DC \\perp AB$ and $DE$ is a second diameter. What is the ratio of the area of $\\triangle DCE$ to the area of $\\triangle ABD$?\n\n
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\n\n$\\mathrm{(A) \\ } \\frac{1}{6} \\qquad \\mathrm{(B) \\ } \\frac{1}{4} \\qquad \\mathrm{(C) \\ } \\frac{1}{3} \\qquad \\mathrm{(D) \\ } \\frac{1}{2} \\qquad \\mathrm{(E) \\ } \\frac{2}{3}$", "description_html": "

Let AB be a diameter of a circle and let C be a point on AB with 2\\cdot AC=BC . Let D and E be points on the circle such that DC \\perp AB and DE is a second diameter. What is the ratio of the area of \\triangle DCE to the area of \\triangle ABD ?

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\\mathrm{(A) \\ } \\frac{1}{6} \\qquad \\mathrm{(B) \\ } \\frac{1}{4} \\qquad \\mathrm{(C) \\ } \\frac{1}{3} \\qquad \\mathrm{(D) \\ } \\frac{1}{2} \\qquad \\mathrm{(E) \\ } \\frac{2}{3}

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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