Mathematics - Circle Question with Solution | TestHub

MathematicsCircleEquation of chord with given middle point Chord of contact Pair of TangentsMedium2 minPYQ_2020

MathematicsMediumsingle choice

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

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Answer:

Solution:

$L = \sqrt{S_{1}} = \sqrt{16} = 4$
$R = \sqrt{16 + 4 - 16} = 2$
Length of chord of contact $= \frac{2 L R}{\sqrt{L^{2} + R^{2}}} = \frac{2 \times 4 \times 2}{\sqrt{16 + 4}} = \frac{16}{\sqrt{20}}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Equation of chord with given middle point Chord of contact Pair of Tangents

⏱ 2mℹ️ Source: PYQ_2020

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