If the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{gx}+2\mathrm{fy}+\mathrm{c}=0$ bisects the circumference of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+2{\mathrm{g}}^{\mid }\mathrm{x}+2{\mathrm{f}}^{\mathrm{\prime }}\mathrm{y}+{\mathrm{c}}^{\mid }=0$ then the length of the common chord of the circles is 

  From the given data common chord passes through centre of second circle so first circle bisects second circle

 length of the chord = diameter of the 2nd circle 
$=2{\sqrt{\mathrm{g}{\text{'}}_{ }^2+{\mathrm{f}}_{ }^{\text{'}2}-c^{\text{'}}}}^{ }$