locus wanted, circumcircle, incircle (Kyiv City Olympiad 2007 10.3)
Source:
June 29, 2020
geometrycircumcircleincircleangle bisectorLocus
Problem Statement
The points are given on the plane, which are the points of intersection of the angle bisector of some triangle with an inscribed circle, and the point is the intersection of the angle bisector with a circumscribed circle other than the vertex .
a) Find the geometric locus of the possible location of the vertex of the triangle .
b) Find the geometric locus of the possible location of the vertex of the triangle .