# Pentagonal Recursion

Geometry Level 5

The diagonals of a regular pentagon are drawn, yielding a smaller pentagon within. The ratio of the side of the larger pentagon to the side of the smaller pentagon has the form $$\frac {a + \sqrt{b}}{c}$$, where $$a, b$$ and $$c$$ are nonnegative integers and $$a$$ and $$c$$ are coprime. What is $$a+b+c$$?

Details and assumptions

$$b$$ can be a multiple of a square number, $$a$$ can be 0, and $$c$$ can be 1. If you calculate the ratio to be $$2\sqrt{3} = \frac { 0 + \sqrt{12} } {1}$$, then your answer should be $$0 + 12 + 1 = 13$$.

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