Current location - Training Enrollment Network - Mathematics courses - Learning to Practice Excellence is the first volume of P70, the ninth grade junior middle school mathematics education edition. Question 16? Solution process
Learning to Practice Excellence is the first volume of P70, the ninth grade junior middle school mathematics education edition. Question 16? Solution process
The moving circles of (1)O and M (2 2,2)

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.