Question

The ratio of the areas if the in-circle and the circum-circle of a square is-

Answer 1

let the side of square be a
diameter of inner circle=a
radius of inner circle=a/2,r
diameter of circumscribed circle=a✓2,R, diagonal of circle.
radius of circumscribed circle=a✓2/2
Ratio of their are, Larger circle/Smaller circle =πR²/πr² = R²/r²=(a✓2)²/a²
2a²/a² = 2/1
So, their ratio is 2:1