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. $\sqrt{\frac{17}{3}}$
• B. $\frac{4}{5}\sqrt{21}$
• C. $11$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{4}{5}\sqrt{21}$

$AB=?$

$r=\sqrt{(3{)}^2+(4{)}^2-21}=\sqrt{4}=2$

the equation of $AB$ cord of contact is

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

$AM=\sqrt{A{C}^2-C{M}^2}$ $3x+4y-21=0$

$=\sqrt{4-\frac{16}{25}}=\frac{2}{5}\sqrt{21}CM=\frac{3\times 3+4\times 4-21}{\sqrt{9+16}}=\frac{4}{5}$

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