VN-TST 1992 Problem 3

Let $ABC$ a triangle be given with $BC = a$ , $CA = b$ , $AB = c$ ( $a \neq b \neq c \neq a$ ). In plane ( $ABC$ ) take the points $A'$ , $B'$ , $C'$ such that:

I. The pairs of points $A$ and $A'$ , $B$ and $B'$ , $C$ and $C'$ either all lie in one side either all lie in different sides under the lines $BC$ , $CA$ , $AB$ respectively;

II. Triangles $A'BC$ , $B'CA$ , $C'AB$ are similar isosceles triangles.

Find the value of angle $A'BC$ as function of $a, b, c$ such that lengths $AA', BB', CC'$ are not sides of an triangle. (The word "triangle" must be understood in its ordinary meaning: its vertices are not collinear.)