Mathematics · Properties of Triangles

Consider the following statements: 1. In an acute-angled triangle, the orthocentre lies inside the triangle, but in an obtuse-angled triangle, it lies outside. 2. The centroid of a triangle always lies inside the triangle, regardless of its type. 3. In a right-angled triangle, the circumcentre coincides with the orthocentre. Which of the above statements is/are correct?