Collinearity of an Orthocenter, the Incenter, and the Circumcenter
Let ABC be a triangle with incenter I and circumcenter O. Let the incircle intersect AB, BC, and CA at M, N, and P, respectively. Let the orthocenter (the intersection of the altitudes) of MNP be H. Then H, I, and O are collinear.
See Example 6 on page 4 of Mathematical Excalibur, Volume 9, No. 2.