Prove that the radical axis of the circl...

Prove that the radical axis of the circles `x^2+y^2+2gx +2fy+c=0` and `x^2+y^2+2g'x + 2f'y+c'=0` is the diameter of the later circle (or the former bisects the circumference of the later ) if 2g'(g-g')+2f'(f-f')=c-c'

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