Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 1"
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Latest revision as of 09:22, 4 April 2012
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
