If the circle $x^2+y^2+2gx+2fy+c=0$ cuts the three circles $x^2+y^2−5=0$, $x^2+y^2−8x−6y+10=0$ and $x^2+y^2−4x+2y−2=0$ at the extremities of their diameters, then which of the following are true ?
$c=-5$
$fg=147/25$
$g+2f=c+2$
$4f=3g$
Can't think of a simple method.Help please!