Question

If a circle passing through the point $(-1,0)$ touches $y$-axis at $(0,2)$ then the length of the chord of the circle along the $x$ -axis is :

• A. $\frac{3}{2}$
• B. $3$
• C. $\frac{5}{2}$
• D. $5$

Answer 1

The correct option is B $3$

$\begin{array}{c}{\left(OB\right)}^2=r^2\\ {\left(r-1\right)}^2+2^2=r^2\\ r^2-2r+1+4=r^2\\ 2r=5\\ r=\frac{5}{2}\\ BD=\sqrt{r^2-4}\\ =\sqrt{\frac{25}{4}-4}\\ BD=\frac{3}{2}\\ BE=3\\ Hence,optionBiscorrectanswer.\end{array}$