Length of the common chord 2√r2−P.D.2 Circle S′=x2+y2−2ax−2by+a2+b2−c2=0 S"=x2+y2−2bx−2ay+a2+b2−c2=0 Common chord is S' - S" = =2(b−a)x+2(a−b)y=0 =2(b−a)x−2(b−a)y=0 S′−S"=x−y=0 P.D. from C1(a,b)tox−y=0 is P.D.=
a−b
√2
r=√a2+b2−a2−b2+c2=c Length of the common chord = 2√r2−P.D.2 =2√c2−