Get a and b on the vertical line of OM.

The equation of the straight line OM is y = x, and the midpoint E coordinate of OM is (1, 1).

Then the equation of straight line AB is Y =-X+B. Passing through E.

Substitute B=2.

So the equation of line AB is y=-x+2. Intersect the x axis and the y axis.

Intersecting with the x axis, when y=0 and x=2, OA=2.

Intersecting with the Y axis, when x=0 and y=2, OB=2.

So OA+OB=4.

(2) Let the center coordinate of the inscribed circle of △BOA be (m, n).

There is m 2 = n 2.

The midpoint coordinates of AB are (1, 1).

Then m 2 = (1-m) 2+( 1-n) 2.

Calculate m = √ 2/( 1+√ 2) = 2-√ 2, and n = 2-√ 2.

Diameter d 2 = m 2+n 2, and d is a constant value

AB 2 = OA 2+OB 2 = 2 √ 2 is a constant value.

So d+AB= fixed value.