设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r>0),当M∩N=空集时,求实数r的取值范围

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设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r>0),当M∩N=空集时,求实数r的取值范围
设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r>0),当M∩N=空集时,求实数r的取值范围

设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r>0),当M∩N=空集时,求实数r的取值范围
M={(x,y)|x^2+y^2=4},
N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r>0)
M∩N= ø
C:(x-1)^2+(y-1)^2=r^2:
circle ,center C(1,1),radius = r
C1:x^2+y^2=4
circle,center C1 (0,0),radius = 2
CC1 = √(1+1) = √2
M∩N= ø
=> r+2 < CC1 = √2
r < √2 -2 #