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(B) The equations of the circles are $S_1: x^2+y^2+2x+2y+1=0$ and $S_2: x^2+y^2+4x+3y+2=0$. The equation of the common chord is given by $S_1 - S_2 =

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$\frac{1}{\sqrt{5}}$

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(B) The equations of the circles are $S_1: x^2+y^2+2x+2y+1=0$ and $S_2: x^2+y^2+4x+3y+2=0$. The equation of the common chord is given by $S_1 - S_2 = 0$. $(x^2+y^2+2x+2y+1) - (x^2+y^2+4x+3y+2) = 0$. $-2x-y-1=0$,which simplifies to $2x+y+1=0$. The center of circle $S_1$ is $(-1, -1)$ and its radius $r_1 = \sqrt{(-1)^2+(-1)^2-1} = \sqrt{1+1-1} = 1$. The perpendicular distance $d$ from the center $(-1, -1)$ to the line $2x+y+1=0$ is $d = \frac{|2(-1)+(-1)+1|}{\sqrt{2^2+1^2}} = \frac{|-2|}{\sqrt{5}} = \frac{2}{\sqrt{5}}$. The length of the common chord is $2\sqrt{r_1^2-d^2} = 2\sqrt{1^2-(\frac{2}{\sqrt{5}})^2} = 2\sqrt{1-\frac{4}{5}} = 2\sqrt{\frac{1}{5}} = \frac{2}{\sqrt{5}}$. The common chord is the diameter of the required circle,so its diameter $D = \frac{2}{\sqrt{5}}$. The radius of the required circle is $R = \frac{D}{2} = \frac{1}{\sqrt{5}}$.

The radius of the circle whose diameter is the common chord of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2+4x+3y+2=0$ is

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