The \( \mathrm{x} \)-coordinate of the incentre of the triangle tha...

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The \( \mathrm{x} \)-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 :
\( \mathrm{P} \)
(1) \( 2+\sqrt{2} \)
(2) \( 2-\sqrt{2} \)
(3) \( 1+\sqrt{2} \)
(4) \( 1-\sqrt{2} \)
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