RU-ALLRUSSIAN 1981 Problem 15

ABC is a triangle. A' lies on the side BC with $\mathrm{BA} / \mathrm{BC} = 1 / 4$ . Similarly, B' lies on the side CA with $\mathrm{CB} / \mathrm{CA} = 1 / 4$ , and C' lies on the side AB with $\mathrm{AC} / \mathrm{AB} = 1 / 4$ . Show that the perimeter of A'B'C' is between 1/2 and 3/4 of the perimeter of ABC.