in Quantitative Aptitude
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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?

  1. $\frac{\pi}{4}$
  2. $\frac{3\pi}{2}$
  3. $\frac{\pi}{2}$
  4. ${\pi}$
in Quantitative Aptitude
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1 Answer

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inner circle perimeter 2⊼x

then length of PQ is 2x

perimeter of PQRS =4x

then SQ= √((2x)^2 +(2x)^2) =2√2x

SO =√2x

perimeter of outer circle = 2 ⊼ (√2x ) =2√2 ⊼ x

perimeter of ABCD=√2x *4 =4√2x

ratio of perimeter of outer circle : perimeter of ABCD = ⊼ / 2

Ans C)

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