What will be the ratio of the area of the bigger circle to that of the smaller circle in the following figure?

Question

A square is inscribed in a circle and a circle is inscribed in that square. What will be the ratio of the area of the bigger circle to that of the smaller circle?

Answer 1

Area of bigger circle =A1=piR^2
Diagonal of square =dia. Of bigger circle =2R
Side of square =s
s^2 +s^2 =(2R)^2
=>s=R(squareroot2)
Dia.of small circle =r=side of square =s
r=s=R(squareroot2)
Area of smaller circle A2
=pir^2=2piR^2...(put value of r)
Now,
A1/A2=piR^2/2piR^2=1/2
Ans is 1:2

Answer 2

Let L = side of square
Area of inner circle is calculated as follows:
Area = PI * (L/2)^2
Area of bigger circle is calculated as follow:
Radius of bigger circle equal to half of the square´s diagonal (L * Squareroot 2) / 2
Then Area = PI * ((L*Squareroot2)/2)^2
ratio = Area of bigger circle/Area of inner circle = PI * (( L* squarerroty2/2)^2 / PI * (L/2)^2 = 2
The answwer is 2