Question

Angle between tangents drawn from a point P to circle $x^2+y^2-4x-8y+8=0$ is ${60}^o$ then length of chord of contact of P is?

• A. $6$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is A $6$

$x^2+y^2-4x-8y+8=0$

centre $(2,4)$ radiys $=\sqrt{(2{)}^2+(4{)}^2-8}$

$=\sqrt{4+16-8}=\sqrt{12}$

$=2\sqrt{3}$

$QS=2\sqrt{3}\cos {30}^2=2\times \sqrt{3}\times \frac{\sqrt{3}}{2}=3$

$\therefore QR=2\left(QS\right)=2\times 3=6$