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A B C D is a square of unit area. A circ...

`A B C D` is a square of unit area. A circle is tangent to two sides of `A B C D` and passes through exactly one of its vertices. The radius of the circle is (a) `2-sqrt(2)` (b) `sqrt(2)-1` (c) `sqrt(2)-1/2` (d) `1/(sqrt(2))`

A

`2-sqrt(2)`

B

`sqrt(2)-1`

C

`1//2`

D

`1/sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
1
From the figure,
`2(1-r)^(2)=r^(2)`
or `sqrt(2)(1-r)=r`
or `r(sqrt(2)+1)=sqrt(2)`
or `r=(sqrt2)/(sqrt(2)+1)=sqrt(2)(sqrt(2)-1)=2-sqrt(2)`
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