The length of the tangent drawn from any point on the circle $x^2+y^2+2 g x+2 f y+c_1=0$ to the circle $x^2+y^2+2 g x+2 f y+c_2=0$ is

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Aicharya · Accepted Answer

Circles are $\begin{aligned} & C_1 \equiv x^2+y^2+2 g x+2 f y+c_1=0 \ \text {and } & C_2 \equiv x^2+y^2+2 g x+2 f y+c_2=0 \end{aligned}$ Clearly circles are concentric, Clearly, length of tangent is $\begin{aligned} A T & =\sqrt{A O^2-O T^2}=\sqrt{r_1^2-r_2^2} \ & =\sqrt{\left(g^2+f^2-c_1\right)-\left(g^2+f^2-c_2\right)}=\sqrt{c_2-c_1} \end{aligned}$

The length of the tangent drawn from any point on the circle \(x^2+y^2+2 g x+2 f y+c_1=0\) to the circle…

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