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Area of circle inscribed with 3 smaller circles

  1. Jun 22, 2011 #1
    1. The problem statement, all variables and given/known data
    A large circle is inscribed with 3 smaller circles, eachhttps://www.physicsforums.com/newthread.php?do=newthread&f=156 [Broken] of the four circles is tangent to the other three. If the radius of each of the smaller circles is a, find the area of the largest circle.

    2. Relevant equations



    3. The attempt at a solution
    _
    the answer must be 1/3pi(7+4√3)a²
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jun 22, 2011 #2

    lanedance

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    Hi rayrenz - is there a question here ?

    if its just to check you work, then you need to show how you got to the answer
     
  4. Jun 22, 2011 #3

    lanedance

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    ok, so what ideas do you have?
     
  5. Jun 22, 2011 #4
    that's the problem to this, to show the solution on how to arrive the answer with r=a
     
  6. Jun 22, 2011 #5
    maybe find the area of the triangle that connects the center of the three circles
     
  7. Jun 22, 2011 #6

    lanedance

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    not the area, but that triangle is a good place to start... at the end of the day, you want to find the radius R of the large circle

    now back to that triangle... it will be an equilateral triangle - what is the length of one side?
     
  8. Jun 22, 2011 #7

    lanedance

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    then find the distance form the point of a triangle to both the large circle centre and edge, thus giving R
     
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