Let `A_0A_1A_2A_3A_4A_5` be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths the line segments `A_0A_1, A_0A_2` and `A_0A_4` is

Options

A. `3//4`
B. `3sqrt3`
C. 3
D. `3sqrt3//2`

Answer

C

Explanation

Let O be the center of the circle.
`angleA_0OA_1=(360^(@))/6=60^@`
Thus, `A_0OA_1` is an equilateral triangle. we get
`A_0OA_1 (" radius of circle = 1")`
Also `A_0OA_2=A_0OA_4`
`=2A_0D`
`=2(OA_0sin60^@)`
`=2(1)sqrt3/2=sqrt3`
`:. (A_0A_1)(A_0A_2)(A_0A_4)`
`=(1)(sqrt3)(sqrt3)=3`