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Geometry Level 5

Let there exist a triangle \(ABC\) such that \(AB=26\), \(BC=28\) and \(CA = 30\). Let \(AD\) be the internal angle bisector from \(A\) to \(BC\), intersecting \(BC\) at \(D\). Let \(BE\) be the perpendicular from \(B\) to \(AD\), intersecting \(AD\) at \(E\). Let \(G\) be a point on \(BC\) such that \(EG\) is parallel to \(AC\). Find the length of \(DG\) to 2 decimal places.

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