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Magnetic Moment

Let A0A1A2A...

Question

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 $A_{0} A_{1} . A_{0} A_{2} . A_{0} A_{4}$ is

A

\frac{3}{4}

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B

3 \sqrt{3}

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C

3

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D

\frac{3 \sqrt{3}}{2}

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Solution

The correct option is D $3$
Given $A_{0} A_{1} A_{2} A_{3} A_{4} A_{5}$ is a regular hexagon inscribed in a circle of unit radius
$\Rightarrow A_{0} A_{1} = 1$
$\Rightarrow A_{0} A_{2} = 2 sin 60^{0} = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}$
$\Rightarrow A_{0} A_{4} = 2 sin 60^{0} = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}$
$∴ A_{0} A_{1} . A_{0} A_{2} . A_{0} A_{4} = 1 \times \sqrt{3} \times \sqrt{3} = 3$

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