Let $A_{1} A_{2} A_{3} . . . . A_{9}$ be a nine-sided regular polygon with side length $2$ units. The difference between the lengths of the diagonals $A_{1} A_{5}$ and $A_{2} A_{4}$ equals.

2 + \sqrt{12}

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\sqrt{12} - 2

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6

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2

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Solution

The correct option is D $2$
From the figure, difference between $A_{1} A_{5}$ and $A_{2} A_{4}$ is given by
$2 cos 60^{o} + 2 cos 60^{o} = 2$ units.

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A_{1} A_{2} A_{3} . . . . A_{9}

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The difference between an exterior angle of a regular polygon of n-sides with a regular polygon of (n + 2) sides is 6^o. The value of n is

2

n

(n + 1)

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