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Length of Chord of Contact

Tangents are ...

Question

Tangents are drawn from (4, 4) to the circle $x^{2} + y^{2} - 2 x - 2 y - 7 = 0$ to meet the circle at A and B. The length of the chord AB is

$2 \sqrt{3}$

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$3 \sqrt{2}$

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$2 \sqrt{6}$

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$6 \sqrt{2}$

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Solution

The correct option is B
$3 \sqrt{2}$

chord of contact of A(4, 4) w.r.t the circle is x+y - 5 = 0

length of the chord = $2 \sqrt{r^{2} - d^{2}}$ = $2 \sqrt{9 - \frac{9}{2}} = 3 \sqrt{2}$

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