Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

Answer: Option B

According to question

Let the radius of the circle be = $$r$$
∴ DO = OC = $$\frac{r}{2}$$
In right angle ΔAOD
By using Pythagoras theorem
$$\begin{array}{rl}& A{D}^2=O{D}^2+A{O}^2\\ & r^2=\frac{r^2}{4}+A{O}^2\\ & A{O}^2=r^2-\frac{r^2}{4}\\ & A{O}^2=\frac{3r^2}{4}\\ & AO=\frac{\sqrt{3}r}{2}\left(\because AB=2\times AO\right)\\ & AB=\frac{\sqrt{3}r}{2}\times 2\\ & AB=\sqrt{3}r\text{ units}\end{array}$$