The three altitudes of a triangle intersect at a point called the orthocenter of the triangle. Suppose that the vertices of a \(\triangle ABC\) lie on a circle of radius 1 centered at 0. Show that the centroid, the orthocenter and the circumcenter of \(\triangle ABC\) are collinear. This line is called the Euler line of the triangle. Note that the circumcenter of \(\triangle ABC\) is just 0 by our assumption.