Copy of Five circles in a square
The center blue circle is tangent to each of the other blue circles,
which are tangent to the green square. Let the radius of the center circle be R,
and the radius of the other circles be r. Write r as a function of R.
Idea from George Polya Read about George Polya here:
https://en.wikipedia.org/wiki/George_P%C3%B3lya
Write r as a function of R.
What value of R maximizes the area of all 5 circles?
What value of R makes all 5 circles the same area?