Probability — practice question

OAB is a uniform lamina in the form of a quadrant of a circle with centre $O$ and radius $0.8\,\text{m}$, and its centre of mass is at $G.$ The lamina is smoothly hinged at $O$ to a fixed point and can rotate freely in a vertical plane. A horizontal force of magnitude $12\,\text{N}$, acting in the plane of the lamina, is applied at $B.$ The lamina is in equilibrium with $AG$ horizontal (see diagram).