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AP EAMCET202017 Sep 2020Evening ShiftMathematicsCircleActual

The length of the tangent drawn from any point on the circle (x^2+y^2+2 g x+2 f y+c₁=0 ) to the circle (x^2+y^2+2 g x+2 f y+c₂=0 ) is

Options

  1. A( C₂-c₁ )
  2. B( c₁^2+c₂^2 )
  3. C(c₁+c₂ )
  4. D(c₁-c₂ )

Correct answer

A. ( C₂-c₁ )

Step-by-step solution

Circles are ( aligned & C₁ x^2+y^2+2 g x+2 f y+c₁=0 and & C₂ x^2+y^2+2 g x+2 f y+c₂=0 aligned ) Clearly circles are concentric, Clearly, length of tangent is ( aligned A T & = A O^2-O T^2 = r₁^2-r₂^2 & = (g^2+f^2-c₁ )- (g^2+f^2-c₂ ) = c₂-c₁ aligned )

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