Choose the correct option regarding the following statements : Statement I The length of common chord of the circles x^2+y^2+a x+b y+c=0 and x^2+y^2+b x+a y+c=0 equals (a+b)^2-8 c 2 Statement II If two circles intersect at two distinct points, then their radical axis is their common chord.

Step-by-step solution

Statement I The length of common chord of the circles x^2+y^2+a x+b y+c=0 and x^2+y^2+b x+a y+c=0 equals (a+b)^2-8 c 2 Let the circles c ₁ be the center of x^2+y^2+a x+b y+c=0 ...(i) and c₂ be the center of x^2+y^2+b x+a y+c=0 ...(ii) aligned & c₁= ( -a 2 , -b 2 ) & and c₂= ( -b 2 , -a 2 ) aligned r₁= a^2 4 + b^2 4 -c r₁= 1 2 a^2+b^2-4 c aligned & r₂= b^2 4 + a^2 4 -c & r₂= 1 2 a^2+b^2-4 c aligned Radius of both circles is same. c₁ c₂= ( -a 2 + b 2 )^2+ ( -b 2 + a 2 )^2 aligned & (a-b)^2 4 + (a-b)^2 4 & c₁ c₂= a-b