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On a plate in the shape of an equilateral triangle $\text{ABC}$ with area $16\sqrt 3\;\text{sq cm}$, a rod $\text{GD}$, of height $8\:\text{cm}$, is fixed vertically at the centre of the triangle. $\text{G}$ is a point on the plate. If the areas of the triangles $\text{AGD} \:\text{and}\:\text{BGD}$ are both equal to $4\sqrt19;\text{sq cm}$, find the area of the triangle $\text{CGD}\:\text{(in sq cm)}$.

  1. $3 \sqrt {19}$
  2. $4 \sqrt {19}$
  3. $12 \sqrt {3}$
  4. None of these
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