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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.

A

`(sqrt(2)-1)a`

B

`(sqrt(2)+1)a`

C

`(2+sqrt(2)a)`

D

`(2-sqrt(2))a`

Text Solution

Verified by Experts

The correct Answer is:
A
It is evident from the figure that the smallest circle touching all the circles has radius equal to
`OP=OC_(1)-C_(1)P=sqrt(2)a-a= (sqrt(2)-1)a`
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