Let A_0 A_1 A_2 A_3 A_4 A_5 be a regular hexa | vedclass

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(C) The regular hexagon $A_0 A_1 A_2 A_3 A_4 A_5$ is inscribed in a circle of radius $R = 1$. In a regular hexagon,the side length is equal to the rad

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$3$

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(C) The regular hexagon $A_0 A_1 A_2 A_3 A_4 A_5$ is inscribed in a circle of radius $R = 1$. In a regular hexagon,the side length is equal to the radius of the circumscribed circle. Thus,$A_0 A_1 = 1$. To find $A_0 A_2$,consider the triangle $A_0 A_1 A_2$. The interior angle of a regular hexagon is $120^\circ$. Using the Law of Cosines in $	riangle A_0 A_1 A_2$: $A_0 A_2^2 = A_0 A_1^2 + A_1 A_2^2 - 2(A_0 A_1)(A_1 A_2) \cos(120^\circ)$ $A_0 A_2^2 = 1^2 + 1^2 - 2(1)(1)(-\frac{1}{2}) = 1 + 1 + 1 = 3$. So,$A_0 A_2 = \sqrt{3}$. By symmetry,$A_0 A_4 = A_0 A_2 = \sqrt{3}$. The product of the lengths is $A_0 A_1 	imes A_0 A_2 	imes A_0 A_4 = 1 	imes \sqrt{3} 	imes \sqrt{3} = 3$.

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 $A_0 A_1$,$A_0 A_2$,and $A_0 A_4$ is

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