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Let R be the region of the disc x^(2)+y^...

Let R be the region of the disc `x^(2)+y^(2) le 1` in the first quadrant. The the area of the largest possible circile contained in R is

A

`pi(3-2sqrt(2))`

B

`pi(4-3sqrt(2))`

C

`(pi)/(6)`

D

`pi(2sqrt(2)-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Required equation of circle
`(x-h)^(2)+(y-h)^(2)=h^(2)`
Both circle touch internally
`C_(1)C_(2)=|r_(1)-r_(2)|`
`sqrt(h^(2)+h^(2))=|h-1|`
Solve this `h=sqrt(2)-1`
Area `pi(sqrt(2)-1)^(2)=pi(3-2sqrt(2))`
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