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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