The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?
Explanation:
Let the radius of the outer circle be OQ = x.
Hence, perimeter of the circle = 2πx
But OQ = BC = x (diagonals of the square BQCO)
Perimeter of ABCD = 4x
Hence, ratio = 2πx4x=π2.
Hence, option (c).
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