# 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 :$$m+n+o+p$$.

You can try more of my Questions here .

×