Question

There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?

Answer 1

I am trying to write a code to draw pentagon star and have stumbled upon a problem. In the attached diagram, what is the ratio of the diameter of outer (red) circle to the inner (blue) circle. The circles are concentric. I've read that it is ~2.61 but would like to develop the relationship myself.