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Question

Three concentric circles of which biggest is x2+y2=1, have their radii in A.P. If the line y=x+1 cuts all the three circles in real and distinct points, then the interval in which the common difference of AP will lie, is
  1. (0,2122)
  2. (0,2+122)
  3. (0,212)
  4. (0,212)


Solution

The correct option is A (0,2122)
Let the common difference of the radii are r,>0
then the radius of other two circles will be 1r,12r
Now if the line y=x+1 intersects the smallest radius (12r) circle, we can conclude that it will surely intersect the other two circles also
Now for the condition to satisfy 
12r>12,12r>0r(0,2122)

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