Question

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 permissible values of common difference of A.P is/are

• A. $0.4$
• B. $0.6$
• C. $0.01$
• D. $0.1$

Answer 1

The correct option is D $0.1$

Let the radius of the circle are $r_1,r_2$ and 1

line y=x+1

Perpendicular from (0,0) on line y=x+1 = $\frac{1}{\sqrt{2}}$

Now $r_1>\frac{1}{\sqrt{2}}$ but $r_1=1-2d$

hence $1-2d>\frac{1}{\sqrt{2}}\to \frac{\sqrt{2}-1}{\sqrt{2}}>2d\to d<\frac{\sqrt{2}-1}{2\sqrt{2}}$

d=0.1