If perpendiculars be drawn on the sides of a regular polygon of \( n \) sides from any point on the inscribed circle whose radius is \( a\) , then the following conditions hold true :-

\( \frac{2}{n} \times \sum (\frac{p}{a})^{2} = b \)
and
\( \frac{2}{n} \times \sum (\frac{p}{a})^{3} = c \)

- where \( p \) is the length of the perpendicular

Find \( b^{7} + c^{11} \)

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