Let the side of the square ABCD be 2a
A line from the centre will bisect the chords AB, BC, CD and DA
Therefore AP = PB = a. Similarly for other sides too
From the above we can conclude that PQ = QR = RS = SP
PQRS is also a square!
Radius of big circle = diagonal of the square APOS = a
Circumference = 2π* a
Now we have to find the side of square PQRS
We know that radius of small circle = side of the square APOS = a
Consider triangle PSO. PS^{2} = OP^{2} + OS^{2}
PS = a
Circumference of square with side a = 4a
Ratio = 2π* a : 4a
= π : 2
Correct Answer: (A). = π : 2