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The locus of mid-points of the chords of...

The locus of mid-points of the chords of the circle `x^2 - 2x + y^2 - 2y + 1 = 0` which are of unit length is :

A

`(x-1)^(2)+(y-1)^(2)=(3)/(4)`

B

`(x-1)^(2)+(y-1)^(2)=2 `

C

`(x-1)^(2)+(y-1)^(2)=(1)/(4)`

D

`(x-1)^(2)+(y-1)^(2)=(2)/(3)`

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The correct Answer is:
A
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