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KVPY2014MathematicsCircle

Let n 3 and let C₁, C₂, . C_ n , be circles with radii r₁, r₂, , r_ n , respectively. Assume that C_ i and C_ i+1 touch externally for 1 i n-1 . It is also given that the x -axis and the line y=2 2 x+10 are tangential to each of the circles. Then r₁, r₂, , r_ n are in

Options

  1. AAn arithmetic progression with common difference 3+ 2
  2. BA geometric progression with common ratio 3+ 2
  3. CAn arithetic progression with common diffrence 2+ 3
  4. DAgeometric progression with common ratio 2+ 3

Correct answer

D. Ageometric progression with common ratio 2+ 3

Step-by-step solution

Sin = 1 3 = r₁ AP ₁ = r₂ AP ₂ AP ₂= AP ₁+ r ₁+ r ₂ r ₂ 3 = r ₁ 3 + r ₁+ r ₂ r ₂( 3 -1)= r ₁( 3 +1) r₂ r₁ =2+ 3

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