Cool Geometry

Geometry Level 5

A regular pentagon is inscribed in a circle of radius 5 units . P is any point inside the pentagon. Perpendiculars are dropped from P to the sides, or the sides produced, of the pentagon.

The sum of the lengths of these perpendiculars can be expressed in the form \( \frac{ m\sqrt{n} + o}{p} \), where these are all positive integers such that \(o\) and \(p\) are coprime, and \(n\) is not divisible by the square of any prime.

Find the sum :\( m+n+o+p \).

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