In the context of making geometric shapes in AI, I'm wondering what are some of the most efficient ways to achieve a certain shape configuration. For the scope of this question consider a square that has a circle inscribed in it, and that circle also has a square inscribed in it. The result is pictured:
As you can see, I have got it fairly close (when eye-balled anyway). I originally thought I could just click drag and use AI's snap feature to create this type of arrangement of shapes, but that actually didn't pan out. Well, inscribing the circle in the big square worked fine with snaps, but making the smaller square in the circle didn't. There were no snap features to detect when the corners of the square were right on the circle. (Let me know if there is a snap setting for this.) So what I did was resort to the math representation: the diagonal of the square circle is equal to the diameter of the circle -- which is equal to the width of the big square. This ratio when expressed exactly is the square root of 2. With this in mind, I did the following:
select big square > right click > transform > scale > scale UI
As far as I know scale UI only accepts percentages. So to get the percentage I just took an estimation of the square root of two: 1.414, and divided that by 1 to get 70.7%. So I'm exact to at least the tenth place.
Question: Does AI have any kind of fraction or irregular number methods built in? If not, what this the best I can hope for?