Question

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

Answer 1

$E{q}^n$ of chord of contact (coc) from pt $(x_1,y_1)$ is T=0

$\Rightarrow E{q}^n$ of coc from (0,0) is $gx+fy+c=0$ ___ (1)

$E{q}^n$ of coc from (g,f) $gx+fy+g^2+f^2+c=0$ ___ (2)

$E{q}^n$ (1) and (2) are parallel

Distance = $\frac{|c_2-c_1|}{\sqrt{g^2+f^2}}=\frac{|g^2+f^2+c-c|}{\sqrt{g^2+f^2}}=\frac{g^{2}e{t}^2}{\sqrt{g^{2}f{t}^2}}=\sqrt{g^2+f^2}$

Distance = $\sqrt{g^{2}e{t}^2}$