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UKMT Senior Mathematical Challenge, 2020

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Two circles $C_1$ and $C_2$ have their centres at the point $(3,4)$ and touch a third circle, $C_3$ . The centre of $C_3$ is at the point $(0,0)$ and its radius is 2. What is the sum of the radii of the two circles $C_1$ and $C_2$ ?

(A) $6$ (B) $7$ (C) $8$ (D) $9$ (E) $10$

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