Hello, reiward!

Sorry, your friends are right . . .

A square is inscribed in a circle, and another circle is inscribed in the square.

What is the ratio of the *area* of the larger circle to the small circle?

Consider one quadrant of the diagram.

Code:

*
| *
| * B
A * * - - - - *
| * * | *
| * |
| * * | *
| * | *
| * *
O * - - - - - * - - *
C

The radius of the large circle is: .

The area of the large circle is: .

Since is a 45-45-90 right triangle: .

The radius of the small circle is: .

The area of the small circle is: .

The ratio of areas is: .