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

 

S – S¹=0 $\Rightarrow -2x-y-1=0$

$2x+y+1=0$

Equation of required circle is

$x^2+y^2+2x+2y+1+\frac{2\left(-2-1+1\right)}{4+1}$$\left(2x+y+1\right)=0$

$5x^2+5y^2+10x+10y+5-8x-4y-4=0$

$5x^2+5y^2+2x+6y+1=0$

$x^2+y^2+\frac{2}{5}\times +\frac{6}{5}y+\frac{1}{5}=0$

Radius= $\sqrt{\frac{1}{25}+\frac{9}{25}-\frac{1}{5}}=\frac{1}{\sqrt{5}}$