Mathematics · Geometry

Which of the following statements is/are correct regarding the points of concurrency in triangles? I. In an acute-angled triangle, the centroid, circumcenter, and incenter lie inside, but the orthocenter lies outside. II. In an obtuse-angled triangle, the incenter and centroid lie inside, but the orthocenter and circumcenter lie outside. III. In a right-angled triangle, the orthocenter is the midpoint of the hypotenuse.