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Consider four circles (x+-1)^2+(y+-1)^2=...

Consider four circles `(x+-1)^2+(y+-1)^2=1` . Find the equation of the smaller circle touching these four circles.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)+y^(2)=3-2 sqrt(2)`
`A_(1)B_(1)=sqrt(4+4)=2sqrt(2)`
`:. AB=2sqrt(2)-2=2(sqrt(2)-1)`
Thus, the equation of the required circle is` x^(2)+y^(2)= (sqrt(2)-1)^(2)=3-2sqrt(2)`
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