Length of tangent drawn from any point of circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ to the circle $x^{2} + y^{2} + 2 g x + 2 f y + d = 0$ , (d > c) is

\sqrt{c - d}

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\sqrt{d - c}

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\sqrt{g - f}

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\sqrt{f - g}

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Solution

The correct option is B $\sqrt{d - c}$
Let $x_{1}, y_{1}$ be a point on. $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
$\Rightarrow x_{1}^{2} + y_{1}^{2} + 2 g x_{1} + 2 f y_{1} + c = 0$
Length of the tangent = $\sqrt{x_{1}^{2} + y_{1}^{2} + 2 g x_{1} + 2 f y_{1} + d}$ from $(x_{1}, y_{1}) = \sqrt{d - c}$

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