orthocenter, incenter of different triangles and midpoint are collinear
Source: 2017 Oral Moscow Geometry Olympiad grades 10-11 p5
July 25, 2019
geometryincentercollinearorthocenter
Problem Statement
The inscribed circle of the non-isosceles triangle touches sides and at points and , respectively. The circumscribed circle of the triangle intersects the lines and at the points and , respectively. Prove that the orthocenter of triangle , the center of the inscribed circle of triangle and the midpoint of the lie on one straight line.