Forces and equilibrium — practice question

A tiny smooth pulley is fastened at the highest point $A$ of a triangular-prism cross-section $ABC$. The angles are $ABC = 90^\circ$ and $BCA = 30^\circ$. The prism is set up with the face containing $BC$ resting on a horizontal surface. Particles $P$ and $Q$ are joined to the two ends of a light inextensible string, which runs over the pulley. The particles are in equilibrium, with $P$ hanging vertically beneath the pulley and $Q$ touching $AC$ (see diagram). The resultant force exerted on the pulley by the string is $3\sqrt{3}\,\text{N}$.