Question

A pole has to be erected at a point 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 A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

Answer 1

Let P be the required location on the boundary of a circular park such that its distance from gate B is that is BP

Then, AP

In the right triangle ABP we have by using Pythagoras theorem

But the side of right triangle can never be negative

Therefore,

Hence, P is at a distance of from the gate B.