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  •  be a circle of radius one unit, touching both axes. <img alt="\mathrm{{C}_{

\mathrm{{C}_{1}}  be a circle of radius one unit, touching both axes. \mathrm{{C}_{2}}  is another circle that also touches both axes and also touches \mathrm{{C}_{1}} externally, then radius of \mathrm{{C}_{2}} is,

Option: 1

2 \sqrt{2}


Option: 2

3+2 \sqrt{2}


Option: 3

3-\sqrt{2}


Option: 4

3+\sqrt{2}


Answers (1)

best_answer

Equation of \mathrm{C}_{1}(\mathrm{x}-1) 2+(\mathrm{y}-1)^{2}=1

Let equation of \mathrm{C_{2}(x-\alpha)^{2}+(y-\alpha)^{2}=\alpha 2}

Both the circle touches each other

\mathrm{\sqrt{(\alpha-1)^{2}+(\alpha-1)^{2}}=1+\alpha \Rightarrow \alpha=3 \pm 2 \sqrt{2}}

Hence (B) is the correct answer.

Posted by

Pankaj Sanodiya

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