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AP EAMCET202315 May 2023Evening ShiftMathematicsCircleActual

Let A(1,2) be the centre and 3 be the radius of a circle S . Let B(-1,-1) be the centre and r be the radius of another circle S^ . If 3 is the angle between the circles S and S^ , then the number of possible values of r is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

Let C₁=A(1,2), r₁=3 aligned & C₂=B(-1,-1), r₂=r & = (g₁-g₂ )^2+ (f₁-f₂ )^2-r₁^2-r₂^2 2 r₁ r₂ & ( 3 )= (-1-1)^2+(-2-1)^2-3^2-r^2 2 3 r aligned aligned & 1 2 = 4-r^2 6 r 2 r^2+6 r-8=0 & r^2+3 r-4=0 (r-3)(r-1)=0 & r =1,3 aligned

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