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  4. Let the tangents drawn from the origin to the circle, x2 + y2- 8x - 4 y + 16 = 0 touch it at the points A and B. The (AB)2 is equal to :

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Q. Let the tangents drawn from the origin to the circle, $x^2 + y^2- 8x - 4 y + 16 = 0$ touch it at the points A and B. The $(AB)^2$ is equal to :

JEE MainJEE Main 2020Conic Sections

Solution:

$R=\sqrt{16+4-16}=2$
$L=\sqrt{S_{1}}=4$
$AB$(Chord of contact)$=\frac{2LR}{\sqrt{L^{2}+R^{2}}}=\frac{8}{\sqrt{5}}$
$\left(AB\right)^{2}=\frac{64}{5}$

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