Area of circle inscribed with 3 smaller circles

[rayrenz]

Homework Statement

A large circle is inscribed with 3 smaller circles, eachhttps://www.physicsforums.com/newthread.php?do=newthread&f=156 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.

Homework Equations

The Attempt at a Solution

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the answer must be 1/3pi(7+4√3)a²

 

[lanedance]

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

 

[lanedance]

ok, so what ideas do you have?

 

[rayrenz]

that's the problem to this, to show the solution on how to arrive the answer with r=a

 

[rayrenz]

maybe find the area of the triangle that connects the center of the three circles

 

[lanedance]

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?

 

[lanedance]

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