Suppose you're at the center of a circular field of radius 100 ft and there is a guard dog on the perimeter of the field. If the guard dog runs 4 times faster than you but cannot leave the perimeter, how can you avoid the guard dog and escape from the field?
This is an interesting problem and you may want to solve it first if you haven't already seen the solution.
Two questions: Is there a speed multiple at which the guard dog will always be able to catch you and if so what is the multiple?
Given that the dog runs m times faster than you, what is the shortest path to escape from the field?
