Answer Happy

There is a square field ABCD with each side of length 1000 meters. See Figure 1. F is the mid point of side CD and O is the center of the square field. There is a dog standing at each of the points A, B, F, and 0. Although dogs at A,B,0 are free to move, the dog at F is tied to F with a rope of radius 250 meters. So the dog standing at F can not go farther than 250 meters from F. A piece of meat is dropped at a uniformly random location in the square field. Seeing it, each dog starts running towards it at its maximum speed. Maximum speed at which a dog can run is the same for each of these 4 dogs. The dog that grabs the piece of meat is the one that reaches it first. Let PA, PB, Po, Pp be respectively the probability that dog at location A, B,0, F grabs the piece of meat. What are PA, PB, Po, and PF ? B 1000 meters F D 1000 meters Figure 1: Square Field. PA PB Po PF Answer: 1/8 1/8 3/4 – 7/32 - 1/32