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

Question

anonymous · Answer

Is a calculator necessary here?

anonymous · Answer

|dw:1440340144264:dw|

anonymous · Answer

I want to use Heron's Formula and the Law of Cosines, but my gut tells me there's a simpler way haha

anonymous · Answer

|dw:1440351019348:dw|

anonymous · Answer

You can use Hero's formula to find area

anonymous · Answer

Sure. But then you'll eventually have to find the area of this bit here:|dw:1440340728602:dw|

anonymous · Answer

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 :/