Fox 276 - Solution

Solution to 276 was already known but figure below explains more. By Jim Wilson:

http://www.8foxes.com/

The locus of point P is the arc of a circle. Because the central angle must be twice the subtended arc in measure, the central angle is 60. Thus the major arc has length 10π/6. Since the trajectory would also be over a second arc that is a reflection in AB, the total trajectory is 10π/3.