`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)`1//2` d) `1/(sqrt(2))`

Options

A. `2-sqrt(2)`
B. `sqrt(2)-1`
C. `1//2`
D. `1/sqrt(2)`

Answer

1

Explanation

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)`