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 length of the line segments  $A_0{A}_1,A_0{A}_2$ and  $A_0{A}_4$ is _______

Let O be the center of the circle.

$\mathrm{\angle }{A}_{0}O{A}_1=\frac{{360}^0}{6}={60}^0$

Thus, $A_{0}O{A}_1$ is an equilateral triangle

We get $A_0{A}_1=1$ 1(radius of circle = 1)

Also$A_0{A}_2=A_0{A}_4=2OD=2\left[O{A}_0\right]\sin {60}^{\circ }$

$=2\left(1\right)\frac{\sqrt{3}}{2}=\sqrt{3}\text{. }$

$\therefore \left(A_0{A}_1\right)\left(A_0{A}_2\right)\left(A_0{A}_4\right)=\left(1\right)\left(\sqrt{3}\right)\left(\sqrt{3}\right)=3$