circumcircle, excircle, equal segments, parallel wanted
Source: 2018 Oral Moscow Geometry Olympiad grades 8-9 p3
July 25, 2019
geometrycircumcircleexcircleparallel
Problem Statement
On the extensions of sides and of triangle beyond points and , respectively, the segments and are drawn. A circle is tangent to segment at point , side and the extension of side beyond point . Point is the midpoint of segment . Prove that the line is parallel to the bisector of angle .