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Finding a locus

Source: Czech and Slovak Olympiad 1983, National Round, Problem 6

April 10, 2020
geometrylocus of pointsincircleTriangle

Problem Statement

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