A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

Explanation

To solve the problem, we need to determine if it is possible to erect a pole at a point on the boundary of a circular park with a diameter of 13 meters, such that the difference in distances from two diametrically opposite gates A and B is 7 meters. We will also find the distances from the gates if it is possible.

### Step-by-step Solution:

1. **Understanding the Problem**:
- The diameter of the circular park is given as 13 meters, which means the radius \( r \) is \( \frac{13}{2} = 6.5 \) meters.
- Let the distances from the pole to gates A and B be \( x \) and \( y \) respectively.
- We are given that the difference in distances is \( |x - y| = 7 \) meters.
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