Calculate circle radius with given triangle The following information is given:

Given the legs of red triangle, find R.
Little 'r' is the length of the arc between 2 red intersections with circle.
It is unknown.
Is that possible or the task is not defined correctly ?
If we know the lengths of chord and arc then it is possible. The length of the chord is $d=\sqrt{8^2+6,5^2} \approx 10.31$. Now if we connect ends of the chord with the center of the circle, we will get a sector which has a measure $\theta$. We know that $\theta=\frac{r}{R}$. Thus we have an isosceles triangle formed by two radii and the chord which has vertex angle $\theta$. Draw a height from the center of the circle, the height will be a median and a bisector. This gives us another equation: $\sin \frac{\theta}{2}=\frac{d}{2R}$ or $$\color{blue}{\sin \frac{r}{2R}=\frac{d}{2R}}$$ This equation has one unknown and can be solved using numerical methods.
Assuming $r$ is the length of that arc and that it's given, then it is possible. Otherwise it isn't, since then you can make $R$ arbitrarily large.