An arc can be expressed as (x-1) 2+(y-1) 2 =1,(0

Now we have obtained (x-1) 2+(y-1) 2 =1,

Now it is very simple to find the minimum value of 2(x+y).

Method 1: Triangular substitution, so that x- 1=cosθ, y- 1=sinθ, 0≤θ≤π/2, and then we can solve it quickly.

Method 2: Combination of numbers and shapes, let 2(x+y)=t, that is, y=-x+t/2, then t is the smallest, that is, the intercept t/2 of a straight line on the Y axis is the smallest.

By translating up and down in a straight line, you can see it soon.

Method 3: Basic inequality,

Let 1-x=a and 1-y=b, then (a+b)2= 1+2ab, so 2(a+b)=2√( 1+2ab), A2+B2 =

Finally, it should be ≥4-2√2