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Solution :

`0 = (a+x)/2` <br>
`x=-a` <br>
`1= (b+y)/2` <br>
`y= 2-b` <br>
now,` 1= (-a + 2 -a)/2` <br>
`2 = -2a + 2` <br>
`a= 0` <br>
& `4-2b = 0` <br>
`b=2` <br>
`AC= sqrt((0-2)^2 + (2-0)^2) = sqrt 8 ` <br>
`I_n = (ax_1 + bx_2 + c x_3)/(a+b+c)` <br>
where, a,b,c are length of the sides & `x_1, x_2 , x_3` are opposite vertex coordinates <br>
so,` (2 xx 2 + 2 xx 0 + sqrt8 xx 0)/(2 + 2 + sqrt8)` <br>
`= 4/(4 + 2 sqrt2) xx (4 - 2sqrt 2)/(4 - 2sqrt 2)` <br>
`= (16- 8 sqrt2)/(16- 8)` <br>
`= (16- 8 sqrt2)/8` <br>
`= (4-2sqrt2)/2 = 2 - sqrt2` <br>
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