Question

In order to circumscribe a circle on a triangle, which line must you construct?

Answer 1

We need to construct the perpendicular bisectors of at least two of the three sides.

The perpendicular bisector is the locus of points that ensures equal distance between any point on the line and the two ends of the segment. 

The intersection of the two or three (congruent) perpendicular bisectors is the centre of the circumcircle.