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KVPY2014MathematicsCircle

Let C₀ be a circle of radius 1 .for n 1 , let C_ n be a circle whose area equals the area of a square inscribed in C _ n -1 . Then _ i =0 ^ Area ( C _ i ) equals:

Options

  1. A²
  2. B-2 ²
  3. C1 ²
  4. D² -2

Correct answer

D. ² -2

Step-by-step solution

Let a, a₁, a_ 2-- be the length of siden of square inscribed in circle c₀, c₁, c₂= and r ₁, r ₂, r ₃, _ ---- be radius of circle c ₁, c ₂ , then, a₀²=2= r₁² array l r₁= 2 2 a₁²= 8 a₁²= 4 = r₂² r₂= 2 _ i=0 ^ Area (C i)= . i = +2+ 4 + 8 ² = 1- 2 = ² -2 array

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