2012 AMC 12A Problem 12


A square region ABCDABCD is externally tangent to the circle with equation x2+y2=1x^2+y^2=1 at the point (0,1)(0,1) on the side CDCD . Vertices AA and BB are on the circle with equation x2+y2=4x^2+y^2=4 . What is the side length of this square?

(A) 10+510(B) 255(C) 223(D) 21945(E) 9175\textbf{(A)}\ \frac{\sqrt{10}+5}{10}\qquad\textbf{(B)}\ \frac{2\sqrt{5}}{5}\qquad\textbf{(C)}\ \frac{2\sqrt{2}}{3}\qquad\textbf{(D)}\ \frac{2\sqrt{19}-4}{5}\qquad\textbf{(E)}\ \frac{9-\sqrt{17}}{5}


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

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Category: AMC 12A
Points: 3
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