What is the equation to determine a square in a circle?

Answer 1

Consider a circle of radius r. You want a square inside of that circle.

The diameter of the circle is 2r and this is also the length of the diagonal of the square.

Now the Pythagorean theorem says that if the side of the square inside the circle is of length s.

2s2 =4r2

this come for a2 +b2 =c2

where a and b are s and c is 2r

so we have s2 =2r2

Then length of the side OS the square is

r(square root of 2)

or s=r(square root of 2)