The distance between the chords of contact of tangents to the circle $x^2+y^2+2gx+2fy+c=0$  from the origin and the point  $(g,f)$ is:

Equation of chord of contact of $p(x_1,y_1)$ with respect to the circle $s=0$  is  $s_1=0$
$$\begin{gathered} Chord of contact of (0,0) is gx+fy+c=0 \\ Chord of contact of (g,f) is gx+fy+\frac{g^2+f^2+c}{2}=0 \\ Dis\tan ce between them=\frac{\left|\frac{g^2+f^2+c}{2}-c\right|}{\sqrt{g^2+f^2}}=\frac{\left|g^2+f^2-c\right|}{2\sqrt{g^2+f^2}} \end{gathered}$$