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A pole has to be erected on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $\text{A}$ and $\text{B}$ on the boundary is $7$ meters. The distance of the pole from one of the gates is:

  1. $8$ metres
  2. $8.25$ metres
  3. $5$ metres
  4. None these
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