Consider the following potential location. We have a point that is at distances of 8, 5, and 3 from the respective vertices of a triangle. A different picture would result if we assumed the point was inside the triangle.
Now consider rotating the triangle formed by Poole, Bray, and the Store by 60 degrees around Poole.
Why would this figure result? A new equilateral triangle results and the Store, Alton (also the image of Bray), and the image of the store are collinear after the rotation. Why?
If all else fails, use the law of cosines . . .