The distance between the chords of contact of the tangent to the circle x2+y2+2gx+2fy+c=0from the origin and the point (g,f) is

The equations of chords of contact of the tangents drawn from the origin and the point (g, f) to the given circle are respectively gx+fy+c=0          …(i)and, 2gx+2fy+g2+f2+c=0         …(iii)Clearly, (i) and (ii) are parallel. Therefore, the distance 'd' between them is given by d=g2+f2+c4g2+4f2−c82+f2=g2+f2−c2g2+f2