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