IMO 1974 LL YUG52
A fox stands in the center of the field which has the form of an
IMO 1974 LL YUG52
Origin: YUG
Problem
A fox stands in the center of the field which has the form of an equilateral triangle, and a rabbit stands at one of its vertices. The fox can move through the whole field, while the rabbit can move only along the border of the field. The maximal speeds of the fox and rabbit are equal to u and v, respectively. Prove that: (a) If 2u > v, the fox can catch the rabbit, no matter how the rabbit moves. (b) If 2u \leqv, the rabbit can always run away from the fox.