Mock AIME 3 Pre 2005 Problems/Problem 1

Problem

Three circles are mutually externally tangent. Two of the circles have radii $3$ and $7$ . If the area of the triangle formed by connecting their centers is $84$ , then the area of the third circle is $k\pi$ for some integer $k$ . Determine $k$ .

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Mock AIME 3 Pre 2005 Problems/Problem 1

Problem

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