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The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

( A ) $2 + \sqrt{2}$
( B ) $1 - \sqrt{2}$
( C ) $1 + \sqrt{2}$
( D ) $2 - \sqrt{2}$

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