Midpoints of chords of an excircle through the circumcircle
Source: XVIII Tuymaada Mathematical Olympiad (2011), Junior Level
July 29, 2011
geometrycircumcirclegeometry unsolved
Problem Statement
An excircle of triangle touches the side at and the extensions of sides and at and , respectively. Prove that if the midpoint of lies on the circumcircle of , then the midpoint of also lies on that circumcircle.