Question:
If the length of the chord of the circle, $x^{2}+y^{2}=r^{2}(r>0)$ along the line, $y-2 x=3$ is $\mathrm{r}$, then $\mathrm{r}^{2}$ is equal to :
Correct Option: , 2
Solution:
Let chord
$\mathrm{AB}=\mathrm{r}$
$\because \Delta \mathrm{AOM}$ is right angled triangle
$\therefore \mathrm{OM}=\frac{\mathrm{r} \sqrt{3}}{2}=$ perpendicular distance of line
AB from $(0,0)$
$\frac{r \sqrt{3}}{2}=\left|\frac{3}{\sqrt{5}}\right|$
$r^{2}=\frac{12}{5}$