Final answer:
If the circumcenter and orthocenter of (△ ABC) are collinear with vertex A, the triangle must be a right triangle, where the right angle is at vertex A.
Step-by-step explanation:
In (△ ABC), if the circumcenter and orthocenter are collinear with vertex (A), it suggests a particular relationship between the triangle's sides and angles. The circumcenter is the point where the perpendicular bisectors of the triangle's sides intersect, which is equidistant from all three vertices of the triangle. Meanwhile, the orthocenter is the point where the altitudes of the triangle meet.
When these two points and a vertex are collinear in a triangle, this typically occurs in a right triangle, where the right angle is at vertex A. This is because in a right triangle, the hypotenuse acts as a diameter of the circumcircle; thus, the circumcenter lies at the midpoint of the hypotenuse. And since the altitude from the right angle bisects the hypotenuse, the orthocenter also coincides with this midpoint. Hence, the correct answer is that (△ ABC) must be a right △.