A) \[2<r<8\]
B) \[r=2\]
C) \[r<2\]
D) \[r>2\]
Correct Answer: A
Solution :
[a] : Centres : \[{{C}_{1}}(1,3),{{C}_{2}}(4,-1),\] Radii:\[{{r}_{1}}=r,{{r}_{2}}=\sqrt{16+1-8}=3\] \[{{C}_{1}}{{C}_{2}}=\sqrt{9+16}=5,|{{r}_{1}}-{{r}_{2}}|<{{C}_{1}}{{C}_{2}}<{{r}_{1}}+{{r}_{2}}\] \[\Rightarrow \]\[|r-3|<5<r+3\] \[\therefore \]\[r>2,|r-3|<5\Rightarrow r-3<5,r<8\] \[\therefore \]\[2<r<8\].
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