# Trig +Nested Radicals = Fun

Geometry Level 4

If $$\sqrt{2 + \sqrt{2+\sqrt2}}$$ is in the form of $$A \cos \left( \dfrac BC \pi \right)$$, where $$A,B$$ and $$C$$ are positive integers with $$B,C$$ coprime, find the minimum value of $$A+B+C$$.

Bonus: Investigate why $$\sqrt { 2+\sqrt { 2+\sqrt { 2 \cdots} } } =2$$ using trigonometry.

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