设集合A={(x,y)|m/2≤(x-2)²+y²≤m²,x,y∈R}B={(x,y)|2m≤x+y≤2m+1,x,y∈R},若A交B≠∅,则m的取值范围是

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设集合A={(x,y)|m/2≤(x-2)²+y²≤m²,x,y∈R}B={(x,y)|2m≤x+y≤2m+1,x,y∈R},若A交B≠∅,则m的取值范围是
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设集合A={(x,y)|m/2≤(x-2)²+y²≤m²,x,y∈R}B={(x,y)|2m≤x+y≤2m+1,x,y∈R},若A交B≠∅,则m的取值范围是
设集合A={(x,y)|m/2≤(x-2)²+y²≤m²,x,y∈R}
B={(x,y)|2m≤x+y≤2m+1,x,y∈R},若A交B≠∅,则m的取值范围是

设集合A={(x,y)|m/2≤(x-2)²+y²≤m²,x,y∈R}B={(x,y)|2m≤x+y≤2m+1,x,y∈R},若A交B≠∅,则m的取值范围是
A表示圆环,B表示两平行线间的区域.
A∩B≠∅,
<==>大圆与平行线之一有公共点,
<==>|2-(2m+1)|/√2<=|m|,或|2-2m|/√2<=|m|,
<==>|2m-1|<=√2|m|,或√2|m-1|<=|m|,
平方得4m^2-4m+1<=2m^2,或2(m^2-2m+1)<=m^2,
整理得2m^2-4m+1<=0,或m^2-4m+2<=0,
解得(2-√2)/2<=m<=(2+√2)/2,或2-√2<=m<=2+√2,
求并集得(2-√2)/2<=m<=2+√2,为所求.