CircleHardBloom L3
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 interval in which the common difference of the A.P. will lie is:
Options
A.$\left( 0,\frac{1}{4} \right)$
B.$\left( 0,\frac{1}{2\sqrt{2}} \right)$
C.$\left( 0,\frac{2 - \sqrt{2}}{4} \right)$
D.none
Solution
[Key Concept: Three concentric circles with radii in AP: require the line to cut each in real points (discriminant $> 0$) to bound the common difference.]
For max common difference, the smallest circle just touches the line
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