Collinearity of a triangle's circumcenter, incenter, and the contact triangle's orthocenter

Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle's contact triangle (the triangle formed by the points of contact of the incircle with the sides). Then I, O, and H are collinearComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic