In the diagram, the circle has radius 7 and and centre O. Points A,B and C are on the circle. If ∠BOC=120∘ and AC=AB+1, determine the length of AB.
[asy]
import graph; size(120); real lsf = 0.5; pen dp = linewidth(0.7) + fontsize(10); defaultpen(dp); pen ds = black; pen qqttff = rgb(0,0.2,1); pen xdxdff = rgb(0.49,0.49,1); pen fftttt = rgb(1,0.2,0.2);
draw(circle((2.34,2.4),2.01),qqttff); draw((2.34,2.4)--(1.09,0.82),fftttt); draw((2.34,2.4)--(4.1,1.41),fftttt); draw((1.09,0.82)--(1.4,4.18),fftttt); draw((4.1,1.41)--(1.4,4.18),fftttt);
dot((2.34,2.4),ds); label("O", (2.1,2.66),NE*lsf); dot((1.09,0.82),ds); label("B", (0.86,0.46),NE*lsf); dot((4.1,1.41),ds); label("C", (4.2,1.08),NE*lsf); dot((1.4,4.18),ds); label("A", (1.22,4.48),NE*lsf); clip((-4.34,-10.94)--(-4.34,6.3)--(16.14,6.3)--(16.14,-10.94)--cycle);
[/asy] trigonometrygeometry proposedgeometry