If the circle $x^2 +y^2 +2gx+2fy+c=0$ cuts the three circles
\begin{align}x^2+y^2-5&=0\\ x^2+y^2-8x-6y+10&=0\\ x^2+y^2-4x+2y-2&=0\end{align}
at the extremities of their diameters, then :
A) $c= -5$
B) $fg=\dfrac{147}{25}$
C) $g+2f=c+2$
D) $4f=3g$
Please explain how to do it. The correct options are A,B,D