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
.