1. The figure below shows two concentric circles with centre 0. 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?
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By: anil on 05 May 2019 02.31 am
By symmetry, it is safe to assume that the polygon ABCD is a square. So, AB = PO. The perimeter of the inner square = 4 AB. The perimeter of the outer circle = $$ 2 pi imes AB$$ So, ratio = $$ frac{2 pi imes AB}{4AB}$$ = $$ frac{pi}{2}$$
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