Sorry, I became a little obsessed with the question. This is the code I came up with. It isn't marked up real well and if you're curious how I came up with any numbers, let me know.

void setup(){
size(800,600);
background(0);
frameRate(10);
}

void draw(){
smooth();
circle(random(-width/2,width/2),random(-height/2,height/2),random(20,60));
}

void circle(float x, float y, float size){
pushMatrix();
translate(width/2,height/2);
scale(1,-1);
fill(random(0,255),random(0,255),random(0,255),130);
strokeWeight(1);
stroke(255,160);
ellipse(x,y,size,size);
stem(x,y,size);
popMatrix();
}

void stem(float x, float y, float size){
float radius = size/2;
float dist = sqrt(sq(x)+sq(y));
if (x == 0) {
line(0,0,0,y-radius);
}
else {
float distNew = dist - radius;
float slope = y/x;
float x2 = sqrt(sq(distNew)/(sq(slope)+1));
float y2 = slope*x2;
if (x < 0) {
x2 = -x2;
y2 = -y2;
}
line(0,0,x2,y2);
}
}