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  • Radius of smaller circle that touches the line to (1, 1) and also touches the x–axis is :

Radius of smaller circle that touches the line \mathrm{y=x} to (1, 1) and also touches the x–axis is :

 

Option: 1

2-(\alpha, 0) \sqrt{2}


Option: 2

2+\sqrt{2}


Option: 3

\sqrt{2}-1


Option: 4

1+\sqrt{2}


Answers (1)

best_answer

Since  \mathrm{O A=O P \Rightarrow p \in(\sqrt{2}, 0)}
equation of \mathrm{A C(y-1)=-1(x-1)}

i.e \mathrm{y=-x+2}
equation of \mathrm{P C \quad x=\sqrt{2}}
\mathrm{\Rightarrow C=(\sqrt{2}, 2-\sqrt{2})}

Thus radius is \mathrm{2-\sqrt{2}}



Hence (A) is the correct answer.

Posted by

Divya Prakash Singh

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