A chord on a circle will make up one side of an isosceles triangle, with the other two sides having length equal to the radius [tex]r[/tex] of the circle. So if you know the length of the chord, you can find the central angle subtended by the chord (the angle between the sides with length [tex]r[/tex]).
If the chord has length [tex]x[/tex], then the central angle [tex]\theta[/tex] can be found with some basic trig:
[tex]\sin\dfrac\theta2=\dfrac{\frac x2}r=\dfrac x{2r}[/tex]
Once you find [tex]\theta[/tex], you can find the arc length [tex]L[/tex] using the relation
[tex]\dfrac L\theta=\dfrac{2\pi r}{2\pi}\implies L=r\theta[/tex]
