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Problem Description The ratio of the radii of two concentric circles is \(1:3\). If \(\overline{AC}\) is a diameter of the larger circle, \(\overline{BC}\) is a chord of the larger circle that is tangent to the smaller circle, and \(AB = 12\), then the radius of the larger circle is [asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair O=origin, A=3*dir(180), B=3*dir(140), C=3*dir(0); dot(O); draw(Arc(origin,1,0,360)); draw(Arc(origin,3,0,360)); draw(A--B--C--A); label("\(A\)", A, dir(O--A)); label("\(B\)", B, dir(O--B)); label("\(C\)", C, dir(O--C)); [/asy] $$ \textbf{(A)}\ 13\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 21\qquad\textbf{(D)}\ 24\qquad\textbf{(E)}\ 26 $$

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Solution B

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