2. Example problems II

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 todo so? If yes, at what distances from the two gates should the pole be erected?

 

The pole has to be erected on the boundary of the park at a distance of  $m$ from the gate $B$ and $m$ from the gate $A$.