Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit radius. Then

Question

Let A

_{0}

_{1}

_{2}

_{3}

_{4}

_{5}

be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A

_{0}

_{1}

, A

_{0}

_{2}

and A

_{0}

_{4}

Options:

A . 34

B . 3√3

C . 3

D . 3√32

Answer: Option C
:
C
(c) Each triangle is an equilateral triangle

Let A0A1A2A3A4A5 Be A Regular Hexagon Inscribed In A Circle ...

Hence A

_{0}

_{1}

= 1
A

_{0}

_{0}^{2}

_{0}

_{1}^{2}

_{1}

_{0}^{2}

- 2A

_{0}

_{1}

_{1}

_{2}

cos 120

^{\circ}

= 1 + 1 - 2.1.1(-

\frac{1}{2}

) = 3

\Rightarrow

_{0}

_{2}

\sqrt{3}

_{0}

_{4}

∴

_{0}

_{1}

\times

_{0}

_{2}

\times

_{0}

_{4}

= 1.

\sqrt{3}

\sqrt{3}

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