Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 1"
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Latest revision as of 10:22, 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 |