Question

If OA and OB be the tangents to the circle $x ^ { 2 } + y ^ { 2 } - 6 x - 8 y + 21 = 0$drawn from the origin O, then

AB =

• A. 11
• B. $\frac { 4 } { 5 } \sqrt { 21 }$
• C. $\sqrt { \frac { 17 } { 3 } }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 4 } { 5 } \sqrt { 21 }$

Answer 2

Here the equation of AB (chord of contact) is

$0 + 0 - 3 ( x + 0 ) - 4 ( y + 0 ) + 21 = 0$

$\Rightarrow 3 x + 4 y - 21 = 0$ ….(i)

CM = perpendicular distance from (3, 4) to line (i) is

$\frac { 3 \times 3 + 4 \times 4 - 21 } { \sqrt { 9 + 16 } } = \frac { 4 } { 5 }$

$A M = \sqrt { A C ^ { 2 } - C M ^ { 2 } } = \sqrt { 4 - \frac { 16 } { 25 } } = \frac { 2 } { 5 } \sqrt { 21 }$

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