Maths-
General
Easy

Question

If the squares of the lengths of the tangents from a point P to the circles x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent, x to the power of 2 end exponent plus y to the power of 2 end exponent equals b to the power of 2 end exponent and x to the power of 2 end exponent plus y to the power of 2 end exponent equals c to the power of 2 end exponentare in A.P then a to the power of 2 end exponent comma b to the power of 2 end exponent comma c to the power of 2 end exponent are in

  1. A.P.    
  2. G.P    
  3. H.P    
  4. A.G.P    

The correct answer is: A.P.


    Let p (blank x subscript 1 end subscript comma y subscript 1 end subscript) be any point
    Square of the length of tangent from p (x subscript 1 end subscript comma y subscript 1 end subscript)
    To the circle x to the power of 2 end exponent plus y to the power of 2 end exponent minus a to the power of 2 end exponent equals 0 blank i s blank x subscript 1 end subscript superscript 2 end superscript minus y subscript 1 end subscript superscript 2 end superscript minus a to the power of 2 end exponent
    To the circle x to the power of 2 end exponent plus y to the power of 2 end exponent minus b to the power of 2 end exponent equals 0 blank i s blank x subscript 1 end subscript superscript 2 end superscript plus y subscript 1 end subscript superscript 2 end superscript minus b to the power of 2 end exponent
    To the circle x to the power of 2 end exponent plus y to the power of 2 end exponent minus c to the power of 2 end exponent equals 0 blank i s blank x subscript 1 end subscript superscript 2 end superscript plus y subscript 1 end subscript superscript 2 end superscript minus c to the power of 2 end exponent
    Given that
    x subscript 1 end subscript superscript 2 end superscript minus y subscript 1 end subscript superscript 2 end superscript minus a to the power of 2 end exponent comma x subscript 1 end subscript superscript 2 end superscript minus y subscript 1 end subscript superscript 2 end superscript minus b to the power of 2 end exponent comma x subscript 1 end subscript superscript 2 end superscript minus y subscript 1 end subscript superscript 2 end superscript minus c to the power of 2 end exponent are in A.P
    blank a to the power of 2 end exponent comma blank b to the power of 2 end exponent comma blank c to the power of 2 end exponent are in A.P

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