Join each end of the chord to the centre of the circle to form an isosceles triangle. You will need the length of the radius, r, of the circle and the vertex angle, θ, of the triangle at the centre to find the length of the chord. The perpendicular bisector of this angle splits the triangle into two right triangles. The bisected angle is ½θ and, if the chord length is x, its bisected length is ½x.
By trigonometry ½x/r=sin(½θ), so chord length x=2rsin(½θ).