Three concentric circles of which the biggest is `x^2+ y^2= 1`, have their radii in A.P If the line `y= x+1` cuts all the circles in real and distinct points. The interval in which the common difference of the A.P will lie is:

Answer

`d in (0,(1)/(2)(1-(1))/(sqrt(2))))`

Explanation

If d is the common difference of AP, then the radius of the smallest circle is 1-2d. If the given line y-x-1=0 cuts the smallest circle at real an distinct points, then it will definitely cut the remaining circles at real and distinct points. Therefore,
`(|0-0-1|)/(sqrt(2))lt (1-2d)`
or `1-2dgt (1)/(sqrt(2))`
or` dlt (1)/(2) (1-(1)/(sqrt(2)))`
Hence, `d in (0,(1)/(2)(1-(1)/(sqrt(2))))`