ILL 1974 Problem 52

A fox stands in the centre 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 $2u\le v$ , the rabbit can always run away from the fox.