Given the coordinates of a single point on a circle and a length of an arc $L$, how do I find the coordinates of another point?

Or, to put in another form: I have the radius $r$, the length of the arc $L$ and $({x}_{1},{y}_{1})$ the coordinates. I need to express $({x}_{2},{y}_{2})$ using only $r,L,{x}_{1}$, and ${y}_{1}$.

I'm at a dead end on this.

Or, to put in another form: I have the radius $r$, the length of the arc $L$ and $({x}_{1},{y}_{1})$ the coordinates. I need to express $({x}_{2},{y}_{2})$ using only $r,L,{x}_{1}$, and ${y}_{1}$.

I'm at a dead end on this.