# Hexagon 's Segment

Geometry Level 4

$$ABCDEF$$ is a regular hexagon, with $$AB = 1 \text{ cm}$$. Point $$G$$ lies on $$DC$$, such that $$DG = GC$$. If the length of $$BG$$ is in the form of $$\dfrac{\sqrt{a}}{b} \text{ cm}$$, where $$a,b$$ are coprime positive integer, with $$a$$ isn't a perfect square, find $$a+b$$.

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