A segment $AB$ is fixed on the plane. Consider all acute-angled triangles with side $AB$. Find the locus of а) the vertices of their greatest angles, b) their incenters.
Problem
Source: Sharygin Geometry Olympiad 2017 First Round P5 grades 8-9 [a for 8, b for 8-9]
Tags: geometry, Locus, acute triangle, incenter