In Triangle ABC, the circumcenter and orthocenter are collinear with vertex A. Which of the following statements must be true?
(1) Trinagle ABC must be an isosceles triangle.
(2) Triangle ABC must be an equilateral triangle.
(3) Triangle ABC must be a right triangle.
(4) Traingle ABC must be an isosceles right triangle.
Enter your answer as a comma-separated list. If there is no correct option, write "none".