Thread: an odd PI from dividing circle diameters?

Question:
I want to algebraically find the diameter of a larger circle that has contact with two smaller circles and is bound not to grow larger than x=y (see attached image)

It seems for some reason that if I take 6*(smaller circle)/(larger circle), I get PI. (see attached image)

If I get PI, why do I get PI? Is that normal?

I have serious trouble solving the problem algebraic so I made a script that tries to find the solution. I'm not sure why, but the script is not very precis. I can barely squeeze out the result 3.141

I don't see how I can solve this algebraically when the larger circles diameter is unknown and also position is unknow? how?

I was inspired by the NowIsForevers post here at mathhelpforum:
"A fractal made with circles?"
http://www.mathhelpforum.com/math-he...e-circles.html

here is the script (as3)
[PHP]circl.x =48.0;
circl.y =0;

var h1:Number = 48.0;
var k1:Number = 48.0;

var stepsize:Number = 1.0;

var R1 = h1;
var R2;
var radiusSum;
var dist;
var dir = true;

this.addEventListener(Event.ENTER_FRAME,iter);

function circleSize() {
circl.height = circl.width = circl.x*Math.sqrt(2);
}

function iter(event:Event)
{
circl.x +=stepsize;
circleSize();
checkR1R2();
}

function checkR1R2()
{
R2 = circl.height/2;
radiusSum = R1 + R2;
var val = (h1-circl.x)*(h1-circl.x)+(k1)*(k1)

dist = Math.sqrt(val);

if(dist<radiusSum)
{
updateStepsize(true)
}else{
updateStepsize(false)
}
}

function updateStepsize(val)
{
if(val==dir)
{

}else{
stepsize *=-1;
var rand = Math.random() /1000;
stepsize /=(1.0001+rand);

trace(stepsize);
}
dir=val;
traceQuote();
}

function traceQuote()
{
var bigcirl = circl.height;
var smallcircl = 2*(R1+R1*Math.sqrt(2));
trace("q: " + 6*smallcircl/bigcirl);
}[/PHP]

It was close but no cigar... probably nested in some way, I don't know?

===========================
Assumption that there exists radiuses such that:





We set the smaller radius to one


then:



The larger radius is set such that:




Coordinates:




And the distance d between the coordinates are:\\*









since: