Mock AIME 3 Pre 2005 Problems/Problem 1
Problem
Three circles are mutually externally tangent. Two of the circles have radii and . If the area of the triangle formed by connecting their centers is , then the area of the third circle is for some integer . Determine .
Solution
Let the radius of the third circle be . The side lengths of the triangle are , , and . From Heron's Formula, , or , or . , so . Thus the area of the circle is .
See Also
Mock AIME 3 Pre 2005 (Problems, Source) | ||
Preceded by First Question |
Followed by Problem 2 | |
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