We are given that AB = 5 cm and $$angle$$ AOB = 60° Let us draw OM such that OM $$perp$$ AB.  In right angle triangle AMO, $$sin 30° = dfrac{AM}{AO}$$ $$Rightarrow$$ AO = 2*AM = 2*2.5 = 5 cm. Therefore, we can say that the radius of the circle = 5 cm.  In right angle triangle PNO, $$sin 60° = dfrac{PN}{PO}$$
$$Rightarrow$$ PN = $$dfrac{sqrt{3}}{2}$$*PO = $$dfrac{5sqrt{3}}{2}$$ Therefore, PQ = 2*PN = $$5sqrt{3}$$ cm