Radius of a circumference having two chords In the image, the lenghts of the chords are $6$ and $8$, and the gap between the chords is $1$. Then the radius of the circumference is?

I drew the perpendicular diameters to the chords and tried to apply power of a point, but i didn't find anything. I need some hints. 

By Pythagoras,
$$\sqrt{r^2-3^2}-\sqrt{r^2-4^2}=1$$
then
$$(r^2-3^2)-2\sqrt{r^2-3^2}\sqrt{r^2-4^2}+(r^2-4^2)=1,$$
$$(2r^2-26)^2=4(r^2-9)(r^2-16),$$
$$4r^2-100=0.$$
