CEMC Pascal, 1999

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

Two circles $C_1$ and $C_2$ touch each other externally and the line $l$ is a common tangent. The line $m$ is parallel to $l$ and touches the two circles $C_1$ and $C_3$ . The three circles are mutually tangent. If the radius of $C_2$ is 9 and the radius of $C_3$ is 4, what is the radius of $C_1$ ?

(A) $10.4$ (B) $11$ (C) $8\sqrt{2}$ (D) $12$ (E) $7\sqrt{3}$

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