CZ-SK-MO 1983 Problem 6

Consider a circle $k$ with center $S$ and radius $r$ . Denote $\mathsf M$ the set of all triangles with incircle $k$ such that the largest inner angle is twice bigger than the smallest one. For a triangle $\mathcal T\in\mathsf M$ denote its vertices $A,B,C$ in way that $SA\ge SB\ge SC$ . Find the locus of points $\{B\mid\mathcal T\in\mathsf M\}$ .