A) \[\sqrt{6}\]
B) \[2\]
C) \[\sqrt{2}\]
D) \[3\]
Correct Answer: A
Solution :
Equation of tangent on \[{{C}_{1}}\] at \[(2,1)\] is: \[2x+y-(x+2)-1=0\] \[x+y=3\] If it cuts off the chord of the circle \[{{C}_{2}}\] then the equation of the chord is:\[x+y=3\] Distance of the chord from \[(3,-2)\] \[d=\left| \frac{3-2-3}{\sqrt{2}} \right|=\sqrt{2}\] Length of the chord is \[l=4\] \[{{r}^{2}}=\frac{{{l}^{2}}}{4+{{d}^{2}}}\] where \[r\] is the radius of the circle. \[{{r}^{2}}=4+2=6\] \[\Rightarrow r=\sqrt{6}\]
You need to login to perform this action.
You will be redirected in
3 sec
