2001 Cayley Problem 25

The circle with centre A has radius 3 and is tangent to both the positive x-axis and positive y-axis, as shown. Also, the circle with centre B has radius 1 and is tangent to both the positive x-axis and the circle with centre A. The line L is tangent to both circles. The y-intercept of line L is

\textbf{(A)}\ 3+6\sqrt{3}\quad \textbf{(B)}\ 10+3\sqrt{2}\quad \textbf{(C)}\ 8\sqrt{3}\quad \textbf{(D)}\ 10+2\sqrt{3}\quad \textbf{(E)}\ 9+3\sqrt{3}

If there are no answer choices shown, enter a numerical answer.

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