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Length of Tangent and Power of a Point

The length of...

Question

The length of tangent drawn from the point $(1, 1)$ to the circle $x^{2} + y^{2} + 8 x + 20 y + 70 = 0$ is units.

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Solution

Length of tangent drawn from any point to a given circle is represented by
$L = \sqrt{S_{1}}$
$= \sqrt{1 + 1 + 8 + 20 + 70} = 10$ units

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