# JEE Trigonometry

Geometry Level 5

A regular $$n$$ sided polygon has vertices $$V_1, \ V_2, \ \cdots \ , \ V_n$$.

If $\dfrac{\overline{V_1 V_2}+\overline{V_1 V_3}+ \cdots \cdots +\overline{V_1 V_7}}{\csc {\dfrac{\pi}{n}}}=\overline{V_1 V_2}\left(\dfrac{1+\cot {\dfrac{\pi}{24}}}{2}\right)$ then find the value of $$n$$

$$\textbf{Assumptions and Source}$$

$$\bullet \ \ \ \$$ $$\overline{V_1 V_i}$$ denotes the distance between the first vertex and the $$i^{\text{th}}$$ vertex, where $$V_1$$ is adjacent to $$V_2$$, which is adjacent to $$V_3$$ and so on.

$$\bullet \ \ \ \$$ A similar (but easier) question appeared in the $$1994 \ \text{IITJEE exam}$$.

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