Question

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

• A. 11
• B.
• C.
• D. 12

Answer 1

The correct option is B

Here the equation of AB(chord of contact) is

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

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

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

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

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

$\therefore AB=2AM=\frac{4}{5}\sqrt{21}$