Libgdx - collisions between two moving circles

Question

I've many circles randomly spawned in my screen and moving in different directions. I'm now dealing with collisions between them. The code below just compare any circle on the screen with any other one and should detect collisions by the classic formula. It more or less works, my issue is that I need to use a "magic number" discovered by tries and I can't figure out the reason. (Every circle has the same radius)

Code:

Target item1, item2;
    int magicNumber = 40;
    float dX, dY;
    for (int i = len; --i >= 0;) {
        item1 = activeTargets.get(i);
        for(int j = len; --j >= 0;){
            if(i!=j) {
                item2 = activeTargets.get(j);
                dX = (item1.getPosition().x > item2.getPosition().x) ? item1.getPosition().x - item2.getPosition().x : item2.getPosition().x - item1.getPosition().x;
                dY = (item1.getPosition().y > item2.getPosition().y) ? item1.getPosition().y - item2.getPosition().y : item2.getPosition().y - item1.getPosition().y;
                if ( (dX*dX) + (dY*dY) < (magicNumber*4*item1.body.radius*item1.body.radius) ) {
               // if(item1.body.overlaps(item2.body)) {
                    if(!activeTargets.get(i).collide && !activeTargets.get(j).collide ) {
                        activeTargets.get(i).collide = true;
                        activeTargets.get(j).collide = true;
                        Gdx.app.log("COLLIDE", "Collision between " + activeTargets.get(i).color.toString() + " and " + activeTargets.get(j).color.toString());
                    }
                }
            }
        }
    }