If the length of the chord of the circle,

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 :

  1. $\frac{9}{5}$

  2. $\frac{12}{5}$

  3. 12

  4. $\frac{24}{5}$


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 $(0,0)$

$\frac{r \sqrt{3}}{2}=\left|\frac{3}{\sqrt{5}}\right|$

$r^{2}=\frac{12}{5}$

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