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 \(A\).