SOLUTION: the distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. the area of the largest circle is?

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Question 1178395: the distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. the area of the largest circle is?
Answer by greenestamps(13200) About Me  (Show Source):
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Let the three circles, from largest to smallest, be A, B, and C, with radii a, b, and c, respectively. Then

a+b=14
a+c=12
b+c=10

Add those three equations:

2a+2b+2c=36
a+b+c=18

From that equation and the earlier three equations, we find a=8, b=6, c=4.

So the radius of the largest circle is 8, and so its area is 64pi.

ANSWER: 64pi