I don't have a particularly good reason to want to do this, and I'm just asking out of curiosity.

I am looking for the coordinates of point $\pmb B$, a point on the circumference of a circle.
If I know the following:

1. The equation of the circle (the coordinates of the center $\pmb O$, and its radius $\pmb R$)
2. The coordinates of a point on the circumference, point $\pmb A$
3. The central angle $\widehat{AOB}$ (I know the angle might be useless without trigonometry)
4. The length of the arc $\newcommand{arc}[1]{\stackrel{\Large\frown}{#1}}\arc{AB}$
5. Points $\pmb A$ and $\pmb B$ are both in the upper half of the circle, and the angle $\widehat{AOB}$ is less than $\frac{\pi}{4}$ radians (for this specific example)

Is it possible to find the ccoordinates of $\pmb B$ without using any trigonometric functions (sin,cos,tan,etc)?

I'm not sure how to create an image for this, otherwise I would've included one for clarity.

Edits: I realize that the arc length can be calculated from the central angle and the radius, so point 4 is redundant.
Someone else pointed out that there would be two possible points given the angle and arc length. Would it be possible to find either one or both without using trig?