Let $A_0{A}_1{A}_2{A}_3{A}_4{A}_5$  be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments  $A_0{A}_1,A_0{A}_2,A_0{A}_4$  is

Let  $O$  be the centre of the circle.
 $\angle A_{0}O{A}_1=\frac{360°}{6}=60°$
Thus,  $A_{0}O{A}_1$  is an equilateral triangle. We get  $A_0{A}_1=1$
Also  $A_0{A}_2=A_0{A}_4$
 $$\begin{gathered} =2A_{0}D \\ =2(O{A}_0\sin 60°) \\ =2\left(1\right)\frac{\sqrt{3}}{2}=\sqrt{3} \\ \therefore \left(A_0{A}_1\right)\left(A_0{A}_2\right)\left(A_0{A}_4\right)=\left(1\right)\left(\sqrt{3}\right)\left(\sqrt{3}\right)=3 \end{gathered}$$