Question 1043961: Three circles of radii 8.5, 11.9, and 15.7 cm are mutually tangent.
Find the area bounded by the three circles.
area =
Found 2 solutions by Alan3354, advanced_Learner:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Three circles of radii 8.5, 11.9, and 15.7 cm are mutually tangent.
Find the area bounded by the three circles.
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If you mean the area bounded by the tangent points:
Label the centers:
P - 8.5
Q - 11.9
R - 15.7
The lines between the centers form a triangle PQR.
Label the sides p, q & r, side p opposite angle QPR, etc.
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Find the 3 angles:
Use the Cosine Law:
p^2 = q^2 + r^2 - 2qr*cos(P)
cos(P) = (8.5^2 - 11.9^2 - 15.7^2)/(-2*11.9*15.7) =~ 0.1856233
Angle P =~ 79.3 degs
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Find a 2nd angle the same way.
The 3rd angle is 180 - sum of the 1st 2.
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Find the area of the triangle. Heron's Law will work, or any method.
Subtract the area of each of the 3 sectors.
eg, sector of P = Area of P * (79.3/360)
Answer by advanced_Learner(501)  (Show Source):
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