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In the following figure, the diameter of the circle is $3$ cm. $\text{AB}$ and $\text{MN}$ are two diameters such that $\text{MN}$ is perpendicular to $\text{AB.}$ In addition, $\text{CG}$ is perpendicular to $\text{AB}$ such that $\text{AE : EB} = 1 : 2,$ and $\text{DF}$ is perpendicular to $\text{MN}$ such that $\text{NL : LM} = 1:2.$ The length of $\text{DH}$ in cm is

  1. $2\sqrt{2} -1$
  2. $((2\sqrt{2} -1 ))/2$
  3. $((3\sqrt{2} -1 ))/2$
  4. $((2\sqrt{2} -1 ))/3$
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