three circles with centers A, B and C have respective radii 50, 30 and 20 inches and are tangent to each other externally. Find the area in (in^2) of the curvilinear triangle formed by the three circles

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three circles with centers A, B and C have respective radii 50, 30 and 20 inches and are tangent to each other externally. Find the area in (in^2) of the curvilinear triangle formed by the three circles

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Is a calculator necessary here?
|dw:1440340144264:dw|
I want to use Heron's Formula and the Law of Cosines, but my gut tells me there's a simpler way haha

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|dw:1440351019348:dw|
You can use Hero's formula to find area
Sure. But then you'll eventually have to find the area of this bit here:|dw:1440340728602:dw|
Which involves subtracting the area of this part from the area obtained from Heron's formula:|dw:1440340811064:dw| which needs the interior angles formed from the centres of these three circles and as far as I know, can only be obtained using the law of cosines :/
Does the triangle have to be curved sides? the question says 'curvilinear' triangle
Can you teach me on using the law of cosines in the figure above
Sir, it is the triangle formed inside the three circles
Rein. I have to teach you the law of cosines? XD
I guess it can't be helped. But only for this particular case :D When you know all three sides of a triangle, there is a way to figure out the interior angles, too.
I'm going to need you to play along here, though :) Talking to walls makes me feel weird HAHA
with hero's formula you find the area of triangle PQR by cos formula you can find the angles of triangle. then find the areas of three sectors add them finally subtract from the area of triangle.
find one angle by cos formula to find other angles you can also use sin formula
\[\cos Q=\frac{ PQ^2+QR^2-PR^2 }{ 2PQ*QR }\]
if you want to double check the answer, im getting area around \(142\) : http://www.wolframalpha.com/input/?i=100*%28%5Cint_%7B3%2F2%7D%5E3++4sqrt%283%29-sqrt%2825-%28x-4%29%5E2%29+-+sqrt%289-x%5E2%29%2B+%5Cint_3%5E%7B33%2F7%7D+4sqrt%283%29-sqrt%2825-%28x-4%29%5E2%29+-+sqrt%284-%28x-5%29%5E2%29%29

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