## anonymous one year ago 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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1. anonymous

Is a calculator necessary here?

2. anonymous

|dw:1440340144264:dw|

3. anonymous

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

4. anonymous

|dw:1440351019348:dw|

5. anonymous

You can use Hero's formula to find area

6. anonymous

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

7. anonymous

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 :/

8. anonymous

Does the triangle have to be curved sides? the question says 'curvilinear' triangle

9. anonymous

Can you teach me on using the law of cosines in the figure above

10. anonymous

Sir, it is the triangle formed inside the three circles

11. anonymous

Rein. I have to teach you the law of cosines? XD

12. anonymous

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.

13. anonymous

I'm going to need you to play along here, though :) Talking to walls makes me feel weird HAHA

14. anonymous

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.

15. anonymous

find one angle by cos formula to find other angles you can also use sin formula

16. anonymous

$\cos Q=\frac{ PQ^2+QR^2-PR^2 }{ 2PQ*QR }$