Final answer:
To circumscribe a circle on a triangle, you must construct the perpendicular bisectors of the triangle's sides. These lines intersect at the circumcenter, which is the center of the circumscribed circle.
Step-by-step explanation:
In order to circumscribe a circle on a triangle, the line you must construct is the perpendicular bisector of the sides of the triangle. The perpendicular bisectors of the sides of a triangle will meet at a single point, which is known as the circumcenter. This point is equidistant from all three vertices of the triangle, making it the center of the circumscribed circle. To construct a perpendicular bisector of a side, you need to find the midpoint of that side and then draw a line perpendicular to the side that passes through this midpoint. Doing the same for all three sides will give you the circumcenter, where you can place the compass to draw the circumscribed circle.