A) 3
B) 4
C) 2
D) 1
Correct Answer: B
Solution :
The centres and radii of circles are \[{{C}_{1}}(0,0),{{C}_{2}}(3,4)\] and \[{{r}_{1}}=2,{{r}_{2}}=\sqrt{9+16-24}=1\] Now, \[{{C}_{1}}{{C}_{2}}=\sqrt{{{(3-0)}^{2}}+{{(4-0)}^{2}}}=5\] \[{{r}_{1}}+{{r}_{2}}=2+1=3\] Since, \[{{C}_{1}}{{C}_{2}}>{{r}_{1}}+{{r}_{2}}\] \[\therefore \] Number of common tangents = 4.You need to login to perform this action.
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