Find the length of the common chord of the circles, whose equations are
(x – a)^{2} + y^{2} = a^{2}
x^{2} + (y – b)^{2} = b^{2}
Prove that the equation to the circle whose diameter is this common chord is
(a^{2} + b^{2}) (x^{2} + y^{2}) = 2ab (bx + ay)