exinscribed circle and its tangency pts
Source: Russian olympiad 2003/problem 10.7; IMAR test, october 2003
June 12, 2004
geometrycircumcircleincentertrigonometrygeometric transformationreflectionparallelogram
Problem Statement
The exinscribed circle of a triangle corresponding to its vertex touches the sidelines and in the points and , respectively, and touches its side in the point . Show that if the midpoint of the segment lies on the circumcircle of triangle , then the points , , are collinear, where is the incenter and is the circumcenter of triangle .