A vertex of a triangle concyclic with H, O, I
Source: Kürschák 2002, problem 1
July 8, 2014
geometrycircumcircleincentergeometry unsolved
Problem Statement
We have an acute-angled triangle which is not isosceles. We denote the orthocenter, the circumcenter and the incenter of it by , , respectively. Prove that if a vertex of the triangle lies on the circle , then there must be another vertex on this circle as well.