CEMC Fermat, 2001

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

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

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

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