5. In triangle ABC, let rA be the line that passes through the midpoint of BC and is perpendicular to the internal bisector of ∠BAC. Define rB and rC similarly. Let H and I be the orthocenter and incenter of ABC, respectively. Suppose that the three lines rA, rB, rC define a triangle. Prove that the circumcenter of this triangle is the midpoint of HI. geometryincenterorthocenterCircumcenterangle bisectorBrazilian Math OlympiadBrazilian Math Olympiad 2017