The length of the common chord of the circles (x-a)^2 + (y -b)^2 =c^2 and (x -b)^2 (y-a)^2 =c^2 is ..

Common chord for two circles S₁ and S₂ is given by S₁- S₂ = 0

You can solve this chord’s equation with any one of the equation of circle to the two points, which will help you in geting its length.

Thanks, Vj