touchpoint of incircle, orthocenter and midpoint of altitude collinear wanted
Source: 2022 Oral Moscow Geometry Olympiad grades 8-9 p6
April 17, 2022
geometrycollinearcollinearity
Problem Statement
In an acute non-isosceles triangle , the inscribed circle touches side at point is the midpoint of altitude , is the orthocenter of the triangle formed by the bisectors of angles and and line . Prove that the points and lie on the same line. (D. Prokopenko)