Question

Let the equation of two concentric circles is $x^2+y^2-2x+4y+\lambda =0$. If a chord of first circle is tangent to second circle and normal to a circle passing through centre of these circles and having a centre at $(2,-1)$ is also touching first circle. Then length of chord with respect to first circle is:

• A. $\sqrt{6}$
• B. $2\sqrt{6}$
• C. $3\sqrt{6}$
• D. $4\sqrt{6}$

Answer 1

The correct option is B $2\sqrt{6}$

Radius of third circle is $\sqrt{2}$
Radius of first circle is $2\sqrt{2}$
$\therefore$ Length of chord is:
$2\sqrt{r^2-d^2}=2\sqrt{8-2}=2\sqrt{6}$