The length of the chord, which is tangent to the circle $x^{2} + y^{2} = a^{2}$ with respect to its director circle is

a

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2 a

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2 \sqrt{2} a

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\sqrt{3 a}

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Solution

The correct option is B $2 a$

Equation of the director circle is $x^{2} + y^{2} = 2 a^{2}$
$∴$ Length of the chord $= 2 \sqrt{r^{2} - d^{2}}$
$= 2 \sqrt{2 a^{2} - a^{2}}$
$= 2 a$

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