SOLUTION: three circles are tangent to each other externally. The distance between their centers are 23m, 25m, and 20m respectively.Find the area of the curve between the three circles.

Algebra ->  Circles -> SOLUTION: three circles are tangent to each other externally. The distance between their centers are 23m, 25m, and 20m respectively.Find the area of the curve between the three circles.      Log On


   

Question 536449: three circles are tangent to each other externally. The distance between their centers are 23m, 25m, and 20m respectively.Find the area of the curve between the three circles.
Answer by Alan3354(69443) About Me  (Show Source):
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Find the area of the triangle formed by the 3 centers using Heron's Law.
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Find the 3 angles at the centers.
Use the Cosine Law for 1, then either the Cosine Law or the Law of Sines for the 2nd, then 180 - (sum of 1st 2) for the 3rd.
Find the 3 radii:
r1 + r2 = 25
r1 + r3 = 20
r2 + r3 = 23
--> 9, 11 & 14 for radii
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Find the area of each sector, add them, and subtract from the area of the triangle.