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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
    • one year ago
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    Is a calculator necessary here?

  2. anonymous
    • one year ago
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    |dw:1440340144264:dw|

  3. anonymous
    • one year ago
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    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
    • one year ago
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    |dw:1440351019348:dw|

  5. anonymous
    • one year ago
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    You can use Hero's formula to find area

  6. anonymous
    • one year ago
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    Sure. But then you'll eventually have to find the area of this bit here:|dw:1440340728602:dw|

  7. anonymous
    • one year ago
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    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
    • one year ago
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    Does the triangle have to be curved sides? the question says 'curvilinear' triangle

  9. anonymous
    • one year ago
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    Can you teach me on using the law of cosines in the figure above

  10. anonymous
    • one year ago
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    Sir, it is the triangle formed inside the three circles

  11. anonymous
    • one year ago
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    Rein. I have to teach you the law of cosines? XD

  12. anonymous
    • one year ago
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    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
    • one year ago
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    I'm going to need you to play along here, though :) Talking to walls makes me feel weird HAHA

  14. anonymous
    • one year ago
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    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
    • one year ago
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    find one angle by cos formula to find other angles you can also use sin formula

  16. anonymous
    • one year ago
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    \[\cos Q=\frac{ PQ^2+QR^2-PR^2 }{ 2PQ*QR }\]

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