How do I line up a circle perfectly between 2 curves lines (of others circles)?

Question

For a golden ratio logo I'm trying to put a circle in between the lines of two bigger circles to serve as the head of the eagle, basically where the 'body' ends and the beak can be on top of.

The problem is that no matter how much I try, in many different ways, to line up the blue circle in between the orange and green one, I can't get it to work. It doesn't snap correctly, whether I base it on grid, pixel or points.

If I do this by freehand, I can get pretty close, but I will either end up with the blue circle going outside of the bigger one or end up with some space in between.

And this will result in either having a little bit of space left in between so that the shape builder tool will not cut off the bigger circle and still sees it as one whole, here is an exaggerated example:

or result in the smaller circle going outside of the lines of the bigger circles, meaning that there will be a kink in the curve and not the nice smooth curve that I'm aiming for.

Does anyone know how I would go about this? Or maybe there is a much easier method and I'm trying too hard. Any help is appreciated!

Answer 1

The problem is not to align a circle between two others, or maybe you have the alignment to pixels activated ... whatever

The problem is you are thinking in technical drawing and not in a vector drawing way

• Once you have the two circles, make a perpendicular path where the head ends
• Create a shape using this path as the top side (red in the animation)
• Select the two circles and this shape
• Press Cmd + M Mac or Ctrl + M Win to activate the Shape Builder Tool
• Click inside the two circles to create the head shape
• Get the Direct Selection Tool and select the head corner points
• Use the Live Corner Widget to make them rounded
• Delete the surplus shapes