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A circle with center \( C\) is tangent to the positive \( x\) and \( y\)-axes and externally tangent to the circle centered at \( (3,0)\) with radius \( 1\). What is the sum of all possible radii of the circle with center \( C\)? $$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 9$$
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D
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