Coordinates

Connent the adjecent points together to form a chord. In a cricle the radius is a perpendicular bisector of a chord, therefore:
$A=(-3,-4)\\ B=(3,-4)\\ C=(3,4)\\ \text{we need to find: } O=(x,y)$

Now perp bisector of 

$\overline {AB} \text{ is } x=0\\ \overline{BC}\text{ is } y=0$
$x=0 \text{ and } y=0 \text{ meet at:}\\ \boxed{(0,0)}$